Search for gravitational-wave bursts in the first year of the fifth LIGO science run

B. P. Abbott,17 R. Abbott,17 R. Adhikari,17 P. Ajith,2 B. Allen,2, 60 G. Allen,35 R. S. Amin,21 S. B. Anderson,17

W. G. Anderson,60 M. A. Arain,47 M. Araya,17 H. Armandula,17 P. Armor,60 Y. Aso,17 S. Aston,46 P. Aufmuth,16

C. Aulbert,2 S. Babak,1 P. Baker,24 S. Ballmer,17 C. Barker,18 D. Barker,18 B. Barr,48 P. Barriga,59 L. Barsotti,20

M. A. Barton,17 I. Bartos,10 R. Bassiri,48 M. Bastarrika,48 B. Behnke,1 M. Benacquista,42 J. Betzwieser,17

P. T. Beyersdorf,31 I. A. Bilenko,25 G. Billingsley,17 R. Biswas,60 E. Black,17 J. K. Blackburn,17 L. Blackburn,20

D. Blair,59 B. Bland,18 T. P. Bodiya,20 L. Bogue,19 R. Bork,17 V. Boschi,17 S. Bose,61 P. R. Brady,60

V. B. Braginsky,25 J. E. Brau,53 D. O. Bridges,19 M. Brinkmann,2 A. F. Brooks,17 D. A. Brown,36

A. Brummit,30 G. Brunet,20 A. Bullington,35 A. Buonanno,49 O. Burmeister,2 R. L. Byer,35 L. Cadonati,50

J. B. Camp,26 J. Cannizzo,26 K. C. Cannon,17 J. Cao,20 L. Cardenas,17 S. Caride,51 G. Castaldi,56

S. Caudill,21 M. Cavaglia,39 C. Cepeda,17 T. Chalermsongsak,17 E. Chalkley,48 P. Charlton,9 S. Chatterji,17

S. Chelkowski,46 Y. Chen,1, 6 N. Christensen,8 C. T. Y. Chung,38 D. Clark,35 J. Clark,7 J. H. Clayton,60

T. Cokelaer,7 C. N. Colacino,12 R. Conte,55 D. Cook,18 T. R. C. Corbitt,20 N. Cornish,24 D. Coward,59

D. C. Coyne,17 J. D. E. Creighton,60 T. D. Creighton,42 A. M. Cruise,46 R. M. Culter,46 A. Cumming,48

L. Cunningham,48 S. L. Danilishin,25 K. Danzmann,2, 16 B. Daudert,17 G. Davies,7 E. J. Daw,40 D. DeBra,35

J. Degallaix,2 V. Dergachev,51 S. Desai,37 R. DeSalvo,17 S. Dhurandhar,15 M. Dıaz,42 A. Di Credico,36 A. Dietz,7

F. Donovan,20 K. L. Dooley,47 E. E. Doomes,34 R. W. P. Drever,5 J. Dueck,2 I. Duke,20 J. -C. Dumas,59

J. G. Dwyer,10 C. Echols,17 M. Edgar,48 A. Effler,18 P. Ehrens,17 E. Espinoza,17 T. Etzel,17 M. Evans,20 T. Evans,19

S. Fairhurst,7 Y. Faltas,47 Y. Fan,59 D. Fazi,17 H. Fehrmenn,2 L. S. Finn,37 K. Flasch,60 S. Foley,20 C. Forrest,54

N. Fotopoulos,60 A. Franzen,16 M. Frede,2 M. Frei,41 Z. Frei,12 A. Freise,46 R. Frey,53 T. Fricke,19 P. Fritschel,20

V. V. Frolov,19 M. Fyffe,19 V. Galdi,56 J. A. Garofoli,36 I. Gholami,1 J. A. Giaime,21, 19 S. Giampanis,2

K. D. Giardina,19 K. Goda,20 E. Goetz,51 L. M. Goggin,60 G. Gonzalez,21 M. L. Gorodetsky,25 S. Goßler,2

R. Gouaty,21 A. Grant,48 S. Gras,59 C. Gray,18 M. Gray,4 R. J. S. Greenhalgh,30 A. M. Gretarsson,11

F. Grimaldi,20 R. Grosso,42 H. Grote,2 S. Grunewald,1 M. Guenther,18 E. K. Gustafson,17 R. Gustafson,51

B. Hage,16 J. M. Hallam,46 D. Hammer,60 G. D. Hammond,48 C. Hanna,17 J. Hanson,19 J. Harms,52 G. M. Harry,20

I. W. Harry,7 E. D. Harstad,53 K. Haughian,48 K. Hayama,42 J. Heefner,17 I. S. Heng,48 A. Heptonstall,17

M. Hewitson,2 S. Hild,46 E. Hirose,36 D. Hoak,19 K. A. Hodge,17 K. Holt,19 D. J. Hosken,45 J. Hough,48

D. Hoyland,59 B. Hughey,20 S. H. Huttner,48 D. R. Ingram,18 T. Isogai,8 M. Ito,53 A. Ivanov,17 B. Johnson,18

W. W. Johnson,21 D. I. Jones,57 G. Jones,7 R. Jones,48 L. Ju,59 P. Kalmus,17 V. Kalogera,28 S. Kandhasamy,52

J. Kanner,49 D. Kasprzyk,46 E. Katsavounidis,20 K. Kawabe,18 S. Kawamura,27 F. Kawazoe,2 W. Kells,17

D. G. Keppel,17 A. Khalaidovski,2 F. Y. Khalili,25 R. Khan,10 E. Khazanov,14 P. King,17 J. S. Kissel,21

S. Klimenko,47 K. Kokeyama,27 V. Kondrashov,17 R. Kopparapu,37 S. Koranda,60 D. Kozak,17 B. Krishnan,1

R. Kumar,48 P. Kwee,16 P. K. Lam,4 M. Landry,18 B. Lantz,35 A. Lazzarini,17 H. Lei,42 M. Lei,17 N. Leindecker,35

I. Leonor,53 C. Li,6 H. Lin,47 P. E. Lindquist,17 T. B. Littenberg,24 N. A. Lockerbie,58 D. Lodhia,46 M. Longo,56

M. Lormand,19 P. Lu,35 M. Lubinski,18 A. Lucianetti,47 H. Luck,2, 16 B. Machenschalk,1 M. MacInnis,20

M. Mageswaran,17 K. Mailand,17 I. Mandel,28 V. Mandic,52 S. Marka,10 Z. Marka,10 A. Markosyan,35

J. Markowitz,20 E. Maros,17 I. W. Martin,48 R. M. Martin,47 J. N. Marx,17 K. Mason,20 F. Matichard,21

L. Matone,10 R. A. Matzner,41 N. Mavalvala,20 R. McCarthy,18 D. E. McClelland,4 S. C. McGuire,34 M. McHugh,23

G. McIntyre,17 D. J. A. McKechan,7 K. McKenzie,4 M. Mehmet,2 A. Melatos,38 A. C. Melissinos,54

D. F. Menendez,37 G. Mendell,18 R. A. Mercer,60 S. Meshkov,17 C. Messenger,2 M. S. Meyer,19 J. Miller,48

J. Minelli,37 Y. Mino,6 V. P. Mitrofanov,25 G. Mitselmakher,47 R. Mittleman,20 O. Miyakawa,17 B. Moe,60

S. D. Mohanty,42 S. R. P. Mohapatra,50 G. Moreno,18 T. Morioka,27 K. Mors,2 K. Mossavi,2 C. MowLowry,4

G. Mueller,47 H. Muller-Ebhardt,2 D. Muhammad,19 S. Mukherjee,42 H. Mukhopadhyay,15 A. Mullavey,4

J. Munch,45 P. G. Murray,48 E. Myers,18 J. Myers,18 T. Nash,17 J. Nelson,48 G. Newton,48 A. Nishizawa,27

K. Numata,26 J. O’Dell,30 B. O’Reilly,19 R. O’Shaughnessy,37 E. Ochsner,49 G. H. Ogin,17 D. J. Ottaway,45

R. S. Ottens,47 H. Overmier,19 B. J. Owen,37 Y. Pan,49 C. Pankow,47 M. A. Papa,1, 60 V. Parameshwaraiah,18

P. Patel,17 M. Pedraza,17 S. Penn,13 A. Perraca,46 V. Pierro,56 I. M. Pinto,56 M. Pitkin,48 H. J. Pletsch,2

M. V. Plissi,48 F. Postiglione,55 M. Principe,56 R. Prix,2 L. Prokhorov,25 O. Punken,2 V. Quetschke,47 F. J. Raab,18

D. S. Rabeling,4 H. Radkins,18 P. Raffai,12 Z. Raics,10 N. Rainer,2 M. Rakhmanov,42 V. Raymond,28 C. M. Reed,18

T. Reed,22 H. Rehbein,2 S. Reid,48 D. H. Reitze,47 R. Riesen,19 K. Riles,51 B. Rivera,18 P. Roberts,3

N. A. Robertson,17, 48 C. Robinson,7 E. L. Robinson,1 S. Roddy,19 C. Rover,2 J. Rollins,10 J. D. Romano,42

J. H. Romie,19 S. Rowan,48 A. Rudiger,2 P. Russell,17 K. Ryan,18 S. Sakata,27 L. Sancho de la Jordana,44

V. Sandberg,18 V. Sannibale,17 L. Santamarıa,1 S. Saraf,32 P. Sarin,20 B. S. Sathyaprakash,7 S. Sato,27

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M. Satterthwaite,4 P. R. Saulson,36 R. Savage,18 P. Savov,6 M. Scanlan,22 R. Schilling,2 R. Schnabel,2

R. Schofield,53 B. Schulz,2 B. F. Schutz,1, 7 P. Schwinberg,18 J. Scott,48 S. M. Scott,4 A. C. Searle,17 B. Sears,17

F. Seifert,2 D. Sellers,19 A. S. Sengupta,17 A. Sergeev,14 B. Shapiro,20 P. Shawhan,49 D. H. Shoemaker,20

A. Sibley,19 X. Siemens,60 D. Sigg,18 S. Sinha,35 A. M. Sintes,44 B. J. J. Slagmolen,4 J. Slutsky,21 J. R. Smith,36

M. R. Smith,17 N. D. Smith,20 K. Somiya,6 B. Sorazu,48 A. Stein,20 L. C. Stein,20 S. Steplewski,61 A. Stochino,17

R. Stone,42 K. A. Strain,48 S. Strigin,25 A. Stroeer,26 A. L. Stuver,19 T. Z. Summerscales,3 K. -X. Sun,35

M. Sung,21 P. J. Sutton,7 G. P. Szokoly,12 D. Talukder,61 L. Tang,42 D. B. Tanner,47 S. P. Tarabrin,25

J. R. Taylor,2 R. Taylor,17 J. Thacker,19 K. A. Thorne,19 A. Thuring,16 K. V. Tokmakov,48 C. Torres,19

C. Torrie,17 G. Traylor,19 M. Trias,44 D. Ugolini,43 J. Ulmen,35 K. Urbanek,35 H. Vahlbruch,16 M. Vallisneri,6

C. Van Den Broeck,7 M. V. van der Sluys,28 A. A. van Veggel,48 S. Vass,17 R. Vaulin,60 A. Vecchio,46 J. Veitch,46

P. Veitch,45 C. Veltkamp,2 A. Villar,17 C. Vorvick,18 S. P. Vyachanin,25 S. J. Waldman,20 L. Wallace,17

R. L. Ward,17 A. Weidner,2 M. Weinert,2 A. J. Weinstein,17 R. Weiss,20 L. Wen,6, 59 S. Wen,21 K. Wette,4

J. T. Whelan,1, 29 S. E. Whitcomb,17 B. F. Whiting,47 C. Wilkinson,18 P. A. Willems,17 H. R. Williams,37

L. Williams,47 B. Willke,2, 16 I. Wilmut,30 L. Winkelmann,2 W. Winkler,2 C. C. Wipf,20 A. G. Wiseman,60

G. Woan,48 R. Wooley,19 J. Worden,18 W. Wu,47 I. Yakushin,19 H. Yamamoto,17 Z. Yan,59 S. Yoshida,33

M. Zanolin,11 J. Zhang,51 L. Zhang,17 C. Zhao,59 N. Zotov,22 M. E. Zucker,20 H. zur Muhlen,16 and J. Zweizig17

(The LIGO Scientific Collaboration, http://www.ligo.org)1Albert-Einstein-Institut, Max-Planck-Institut fur Gravitationsphysik, D-14476 Golm, Germany

2Albert-Einstein-Institut, Max-Planck-Institut fur Gravitationsphysik, D-30167 Hannover, Germany3Andrews University, Berrien Springs, MI 49104 USA

4Australian National University, Canberra, 0200, Australia5California Institute of Technology, Pasadena, CA 91125, USA

6Caltech-CaRT, Pasadena, CA 91125, USA7Cardiff University, Cardiff, CF24 3AA, United Kingdom

8Carleton College, Northfield, MN 55057, USA9Charles Sturt University, Wagga Wagga, NSW 2678, Australia

10Columbia University, New York, NY 10027, USA11Embry-Riddle Aeronautical University, Prescott, AZ 86301 USA

12Eotvos University, ELTE 1053 Budapest, Hungary13Hobart and William Smith Colleges, Geneva, NY 14456, USA14Institute of Applied Physics, Nizhny Novgorod, 603950, Russia

15Inter-University Centre for Astronomy and Astrophysics, Pune - 411007, India16Leibniz Universitat Hannover, D-30167 Hannover, Germany

17LIGO - California Institute of Technology, Pasadena, CA 91125, USA18LIGO - Hanford Observatory, Richland, WA 99352, USA

19LIGO - Livingston Observatory, Livingston, LA 70754, USA20LIGO - Massachusetts Institute of Technology, Cambridge, MA 02139, USA

21Louisiana State University, Baton Rouge, LA 70803, USA22Louisiana Tech University, Ruston, LA 71272, USA

23Loyola University, New Orleans, LA 70118, USA24Montana State University, Bozeman, MT 59717, USA

25Moscow State University, Moscow, 119992, Russia26NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA

27National Astronomical Observatory of Japan, Tokyo 181-8588, Japan28Northwestern University, Evanston, IL 60208, USA

29Rochester Institute of Technology, Rochester, NY 14623, USA30Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX United Kingdom

31San Jose State University, San Jose, CA 95192, USA32Sonoma State University, Rohnert Park, CA 94928, USA

33Southeastern Louisiana University, Hammond, LA 70402, USA34Southern University and A&M College, Baton Rouge, LA 70813, USA

35Stanford University, Stanford, CA 94305, USA36Syracuse University, Syracuse, NY 13244, USA

37The Pennsylvania State University, University Park, PA 16802, USA38The University of Melbourne, Parkville VIC 3010, Australia39The University of Mississippi, University, MS 38677, USA

40The University of Sheffield, Sheffield S10 2TN, United Kingdom41The University of Texas at Austin, Austin, TX 78712, USA

42The University of Texas at Brownsville and Texas Southmost College, Brownsville, TX 78520, USA43Trinity University, San Antonio, TX 78212, USA

3

44Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain45University of Adelaide, Adelaide, SA 5005, Australia

46University of Birmingham, Birmingham, B15 2TT, United Kingdom47University of Florida, Gainesville, FL 32611, USA

48University of Glasgow, Glasgow, G12 8QQ, United Kingdom49University of Maryland, College Park, MD 20742 USA

50University of Massachusetts - Amherst, Amherst, MA 01003, USA51University of Michigan, Ann Arbor, MI 48109, USA

52University of Minnesota, Minneapolis, MN 55455, USA53University of Oregon, Eugene, OR 97403, USA

54University of Rochester, Rochester, NY 14627, USA55University of Salerno, 84084 Fisciano (Salerno), Italy

56University of Sannio at Benevento, I-82100 Benevento, Italy57University of Southampton, Southampton, SO17 1BJ, United Kingdom

58University of Strathclyde, Glasgow, G1 1XQ, United Kingdom59University of Western Australia, Crawley, WA 6009, Australia

60University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA61Washington State University, Pullman, WA 99164, USA

(Dated: 27 May 2009)

We present the results obtained from an all-sky search for gravitational-wave (GW) bursts in the64–2000 Hz frequency range in data collected by the LIGO detectors during the first year (November2005 – November 2006) of their fifth science run.The total analyzed livetime was 268.6 days. Multiplehierarchical data analysis methods were invoked in this search. The overall sensitivity expressed interms of the root-sum-square (rss) strain amplitude hrss for gravitational-wave bursts with various

morphologies was in the range of 6 × 10−22 Hz−1/2 to a few ×10−21 Hz−1/2. No GW signals wereobserved and a frequentist upper limit of 3.6 events per year on the rate of strong GW bursts wasplaced at the 90% confidence level. As in our previous searches, we also combined this rate limitwith the detection efficiency for selected waveform morphologies to obtain event rate versus strengthexclusion curves. In sensitivity, these exclusion curves are the most stringent to date.

PACS numbers: 04.80.Nn, 07.05.Kf, 95.30.Sf, 95.85.Sz

I. INTRODUCTION

After many years of preparation, interferometric grav-itational wave (GW) detectors have now begun an eraof long-duration observing. The three detectors ofthe Laser Interferometer Gravitational-Wave Observa-tory (LIGO) [1] reached their design sensitivity levelsin 2005 and began a “science run” that collected datathrough late 2007. This run is called “S5” since it fol-lowed a sequence of four shorter science runs that be-gan in 2002. The German/British GEO600 detector [2]joined the S5 run in January 2006, and the Italian/FrenchVirgo detector [3] began its first science run (denotedVSR1) in May 2007, overlapping the last 4.5 months ofthe S5 run. The data collected by these detectors providethe best opportunity yet to identify a GW signal—thoughdetection is still far from certain—and is a baseline forfuture coordinated data collection with upgraded detec-tors.

Gravitational waves in the frequency band of LIGOand the other ground-based detectors may be producedby a variety of astrophysical processes [4]. See for exam-ple [5] for inspiralling compact binaries, [6] for spinningneutron stars, [7] for binary mergers, and [8, 9, 10, 11]for core-collapse supernovae.

The GW waveform emitted by a compact binary sys-tem during the inspiral phase can be calculated accu-rately in many cases, allowing searches with optimalmatched filtering; see, for example, [12]. The waveformfrom the subsequent merger of two black holes is beingmodeled with ever-increasing success using numerical rel-ativity calculations, but is highly dependent on physi-cal parameters and the properties of strong-field gravity.The uncertainties for the waveforms of other transientsources are even larger. It is thus desirable to exploremore generic search algorithms capable of detecting awide range of short-duration GW signals from poorly-modeled sources—such as stellar core collapse to a neu-tron star or black hole—or unanticipated sources. AsGW detectors extend the sensitivity frontier, it is impor-tant to not rely too heavily on assumptions about sourceastrophysics or about the true nature of strong-field grav-ity, and to search as broadly as possible.

In this paper, we report on a search for GW “burst”signals in the LIGO data that were collected during thefirst 12 months of the S5 science run. A search for GWbursts in the remainder of the S5 data set, along with theVirgo VSR1 data, will be published jointly by the LSCand Virgo collaborations at a later date.

The GW burst signals targeted are assumed to havesignal power within LIGO’s frequency band and dura-

4

tions shorter than ∼1 s, but are otherwise arbitrary. Thisanalysis, like most of our previously published searchesfor GW bursts, focuses on low frequencies—in this case64 Hz to 2000 Hz—where the detectors are the most sen-sitive. A dedicated search for bursts above 2000 Hz ispresented in a companion paper [13].

Interferometric GW detectors collect stable, high-sensitivity (“science mode”) data typically for severalhours at a time, with interruptions due to adverse envi-ronmental conditions, maintenance, diagnostics, and theneed to occasionally regain the “locked” state of the servocontrols. In this analysis we searched the data at all timeswhen two or more LIGO detectors were operating, a de-parture from the all-sky GW burst searches from earlierscience runs [14, 15, 16, 17, 18], which required coinci-dence among three (or more) detectors. In this paper,the term “network” is used to describe a set of detectorsoperating in science mode at a given time. A networkmay include any combination of the Hanford 4 km (H1)and 2 km (H2) detectors, the Livingston 4 km (L1) de-tector and GEO600. Because the GEO600 detector wassignificantly less sensitive than LIGO during the S5 run(a factor of 3 at 1000 Hz, and almost two orders of mag-nitude at 100 Hz), we do not use its data in the initialsearch but reserve it for evaluating any event candidatesfound in the LIGO data.

This paper presents results from three different “anal-ysis pipelines”, each representing a complete search.While the pipelines analyzed the data independently,they began with a common selection of good-quality dataand applied a common set of vetoes to reject identifiableartifacts. Each pipeline was tuned to maximize the sensi-tivity to simulated GW signals while maintaining a fixed,low false alarm rate. No GW signal candidates were iden-tified by any of the analysis pipelines with the chosenthresholds. In order to interpret this non-detection, weevaluate the sensitivity of each pipeline for simulated sig-nals of various morphologies, randomly distributed overthe sky and over time. As expected, there are some sensi-tivity differences among the pipelines, although the sen-sitivities rarely differ by more than a factor of 2 (seesection VII) and no single pipeline performs best for allof the simulated signals considered. We combine the re-sults of the pipelines to calculate upper limits on therate of GW bursts as a function of signal morphologyand strength.

The rest of the paper is organized as follows: Afterspecifying the periods of data, forming the first year ofthe S5 science run in Sec. II, Sec. III describes the state ofthe detectors during that period. Section IV summarizesthe elements of this GW burst search which are commonto all of the analysis pipelines. The analysis pipelinesthemselves are detailed in Sec. V and Appendices C, Dand E. Section VI describes how each pipeline is tuned,while Sec. VII presents the sensitivity curves for simu-lated signals and Sec. VIII describes the systematic er-rors in these sensitivity curves. The results of the searchare given in Sec. IX, and some discussion including esti-

H1 H2

L1

8.4 days2.3%

19.0 days5.1%

27.9 days7.4%

79.0 days21.1%

12.8 days3.4%

15.5 days4.1%

161.3 days43.0%

H1 H2

L1

7.9 days2.1%

20.7 days5.5%

33.8 days9.0%

84.3 days22.5%

9.1 days2.4%

16.7 days4.5%

139.7 days37.2%

FIG. 1: The top diagram indicates the mutually exclusivelivetimes and duty cycles of different networks available fordetection searches. The category 1 and 2 data quality flags(DQF) and vetoes described in Appendices A and B havebeen applied. The bottom diagram indicates the mutuallyexclusive livetimes and duty cycles of the different networksafter category 3 DQF and vetoes have been applied to definethe data set used to calculate upper limits.

mates of the astrophysical reach for burst candidates inSec. X.

II. S5 FIRST-YEAR DATA SET

The search described in this paper uses data from ap-proximately the first calendar year of S5, specifically fromNovember 4, 2005 at 16:00 UTC through November 14,2006 at 18:00 UTC.

Figure 1 shows the amount of science-mode data col-lected (“livetime”) for each mutually-exclusive networkof detectors along with percentages of the experimentcalendar duration (duty cycle). The top Venn diagramrepresents the data with basic data quality and veto con-ditions (see Sec. IV and Appendices A and B), including268.6 days of data during which two or more LIGO de-tectors were in science mode; this is the sample which issearched for GW burst signals. The bottom Venn dia-gram shows the livetimes after the application of addi-tional data quality cuts and vetoes that provide some-what cleaner data for establishing upper limits on GWburst event rates. In practice, only the H1H2L1 andH1H2 (not L1) networks—encompassing most of the live-

5

Frequency [Hz]210 310

]H

z [

stra

in/

1/2

S(f

)

-2310

-2210

-2110

H2

L1

H1LIGO Design

FIG. 2: Representative sensitivities of the LIGO detectorsduring the first year of S5. These curves show the amplitudespectral density of LIGO noise converted to GW strain units.

time, 224 days—are used to set upper limits.

III. THE DETECTORS

A. LIGO

The high sensitivity (see Fig. 2) and duty cycles (78.0%for H1, 78.5% for H2, and 66.9% for L1) achieved dur-ing the S5 run were the result of a number of improve-ments made prior to the run [19, 20]. The major changeswere the successful operation at Livingston of a hydraulicexternal pre-isolator (HEPI) to suppress seismic distur-bances, and the implementation at both sites of a thermalcompensation system (TCS) to reduce thermal lensingeffects in the interferometer arm cavities due to opticalabsorption in mirror coatings and substrates. The HEPIsystem provides a reduction of the seismic noise by anorder of magnitude in the band 0.2–2.0 Hz, and thus sig-nificantly improves the duty cycle of the L1 detector.

Another significant improvement was the extension ofthe wave-front sensing (WFS) subsystem to control allalignment degrees of freedom of the core interferometeroptics, leading to significantly reduced alignment flucta-tions. Several improvements were made to the lengthsensing and control subsystem, enabling the photodetec-tors to take more power without saturation and thus al-lowing the laser power to be increased. A new method tocalibrate the detectors was introduced, based on directactuation of the test masses via radiation pressure froman auxiliary laser beam. Unlike the traditional coil-drivecalibration method [21], which requires rather large testmass displacements, the new technique allows calibrationof the detectors at a level closer to the anticipated signalstrength.

Other improvements included modifications to acous-tic and seismic isolation of optical tables with detectionphotodiodes, changes to the safety shutters to protect

photodiodes from damage when interferometers fall outof lock, and improved detection of impending saturationof photodiodes to prevent lock losses. Finally, a numberof physical effects which led to spurious transients andspectral lines in the data during previous science runshave been diagnosed and mitigated.

B. GEO600

The GEO600 detector, located near Hannover, Ger-many, was also operational during the S5 run, thoughwith a lower sensitivity than the LIGO detectors. TheGEO600 data were not used in the current study as themodest gains in the sensitivity to GW signals would nothave offset the increased complexity of the analysis. TheGEO600 data were held in reserve, and could have beenused to follow up on detection candidates from the LIGO-only analysis.

GEO600 began its participation in S5 on January 21,2006, operating in a night-and-weekend mode. In thismode, science data were acquired during nights and week-ends while commissioning work was performed during theday time. The commissioning work focused mainly ongaining a better understanding of the detector and im-proving data quality. It was performed in a manner thatavoided disrupting science periods and allowed for well-calibrated data to be acquired. Between May 1 and Oc-tober 6, 2006, GEO600 operated in so-called 24/7-mode,during which the detector’s duty cycle in science-modeoperation was maximized and only very short mainte-nance periods took place. Overall in 24/7-mode an in-strumental duty cycle of about 95% and a science-modeduty cycle of more than 90% were achieved. GEO600 re-turned to night-and-weekend mode on October 16, 2006,and work began on further improving the reliability ofthe instrumentation and reducing the glitch rate. Thedetector was operated in night-and-weekend mode un-til the end of S5 in October 2007. Overall, GEO600collected about 415 days of well-calibrated and charac-terized science data in the period between January 2006and October 2007.

IV. ANALYSIS PIPELINE OVERVIEW

In this search for GW bursts, three independent end-to-end analysis pipelines have been used to analyze thedata. These pipelines were developed and implementedseparately, building upon many of the techniques thatwere used in previous searches for bursts in the S1, S2,S3 and S4 runs of LIGO and GEO600 [14, 16, 17, 18, 22],and prove to have comparable sensitivities (within a fac-tor of ∼2; see Sec. VII). One of these pipelines is fullycoherent in the sense of combining data (amplitude andphase) from all detectors and accounting appropriatelyfor time delays and antenna responses for a hypotheti-cal gravitational-wave burst impinging upon the network.

6

This provides a powerful test to distinguish GW signalsfrom noise fluctuations.

Here we give an overview of the basic building blockscommon to all of the pipelines. The detailed operationof each pipeline will be described later.

A. Data quality evaluation

Gravitational-wave burst searches are occasionally af-fected by instrumental or data acquisition problems aswell as periods of degraded sensitivity or nonstationarynoise due to bad weather or other environmental condi-tions. These may produce transient signals in the dataand/or may complicate the evaluation of the significanceof other candidate events. Conditions which may ad-versely affect the quality of the data are catalogued dur-ing and after the run by defining “data quality flags”(DQFs) for lists of time intervals. These DQFs are cat-egorized according to their seriousness; some are usedimmediately to select the data to be processed by theanalysis pipelines (a subset of the nominal science-modedata), while others are applied afterward to veto anyevents found. These categories are described in moredetail in Appendix A.

B. Search algorithms

Data that satisfies the initial selection criteria arepassed to algorithms that perform the signal-processingpart of the search, described in the following section andin three appendices. These algorithms decompose thedata stream into a time-frequency representation andlook for statistically significant transients, or “triggers”.Triggers are accepted over a frequency band that spansfrom 64 Hz to 2000 Hz. The lower frequency cut-off isimposed by seismic noise which sharply reduces sensi-tivity at low frequencies, while the upper cut-off corre-sponds roughly to the frequency at which the sensitivitydegrades to the level found at the low frequency cut-off.(A dedicated search for bursts with frequency contentabove 2000 Hz is presented in a companion paper [13].)

C. Event-by-event DQFs and vetoes

After gravitational-wave triggers have been identifiedby an analysis pipeline, they are checked against addi-tional DQFs and “veto” conditions to see if they occurredwithin a time interval which should be excluded from thesearch. The DQFs applied at this stage consist of manyshort intervals which would have fragmented the dataset if applied in the initial data selection stage. Event-by-event veto conditions are based on a statistical corre-lation between the rate of transients in the GW channeland noise transients, or “glitches”, in environmental andinterferometric auxiliary channels. The performance of

vetoes (as well as DQFs) are evaluated by the extent towhich they remove GW the channel transients of each in-terferometer, as identified by the KleineWelle (KW) [23]algorithm. KW looks for excess signal energy by decom-posing a timeseries into the Haar wavelet domain. Foreach transient, KW calculates a significance defined asthe negative of the natural logarithm of the probabil-ity, in Gaussian noise, of observing an event as energeticor more than the one in consideration. A detailed de-scription of the implementation of the vetoes is given inAppendix B.

D. Background estimation

In order to estimate the false trigger rate from detec-tor noise fluctuations and artifacts, data from the var-ious detectors are artificially shifted in time so as toremove any coincident signals. These time-shifts havestrides much longer than the intersite time-of-flight fora true gravitational-wave signal and thus are unlikely topreserve any reconstructable astrophysical signal whenanalyzed. We refer to these as time-shifted data. Bothunshifted and time-shifted data are analyzed by identicalprocedures, yielding the candidate sample and the esti-mated background of the search, respectively. In orderto avoid any biases, no unshifted data are used in thetuning of the methods. Instead, combined with simula-tions (see below), background data are used as the testset over which all analysis cuts are defined prior to ex-amining the unshifted data-set. In this way, our analysesare “blind”.

E. Hardware signal injections

During the S5 run, simulated GW signals were occa-sionally injected into the data by applying an actuationto the mirrors at the ends of the interferometer arms. Thewaveforms and times of the injections were cataloged forlater study. These were analyzed as an end-to-end val-idation of the interferometer readout, calibration, anddetection algorithms.

F. Simulations

In addition to analyzing the recorded data streamin its original form, many simulated signals are in-jected in software—by adding the signal to the digi-tal data stream—in order to to simulate the passage ofgravitational-wave bursts through the network of detec-tors. The same simulated signals are analyzed by allthree analysis pipelines. This provides a means for es-tablishing the sensitivity of the search by measuring theprobability of detection as a function of the signal mor-phology and strength. These will also be referred to asefficiency curves.

7

V. SEARCH ALGORITHMS

Unmodeled GW bursts can be distinguished from in-strumental noise if they show consistency in time, fre-quency, shape, and amplitude among the LIGO detec-tors. The time constraints, for example, follow from themaximum possible propagation delay between the Han-ford and Livingston sites which is 10 ms.

This S5 analysis employs three algorithms to search forGW bursts: BlockNormal [24], QPipeline [25, 26], andcoherent WaveBurst [27]. A detailed description of eachalgorithm can be found in the appendices. Here we limitourselves to a brief summary of the three techniques. Allthree algorithms essentially look for excess power [28] in atime-frequency decomposition of the data stream. Eventsare ranked and checked for temporal coincidence and co-herence (defined differently for the different algorithms)across the network of detectors. The three techniquesdiffer in the details of how the time-frequency decompo-sitions are performed, how the excess power is computed,and how coherence is assessed. Each analysis pipelinewas independently developed, coded and tuned. Becausethe three pipelines have different sensitivities to differenttypes of GW signals and instrumental artifacts, the re-sults of the three searches can be combined to producestronger statements about event candidates and upperlimits.

BlockNormal (BN) performs a time-frequency decom-position by taking short segments of data and applyinga heterodyne basebanding procedure to divide each seg-ment into frequency bands. A change-point analysis isused to identify events with excess power in each fre-quency band for each detector, and events are clusteredto form single-interferometer triggers. Triggers from thevarious interferometers that fall within a certain coinci-dence window are then combined to compute the “com-bined power”, PC, across the network. These coincidenttriggers are then checked for coherence using CorrPower,which calculates a cross-correlation statistic Γ that wasalso used in the S4 search [17]. A detailed description ofthe BN algorithm can be found in Appendix C.

QPipeline (QP) performs a time-frequency decompo-sition by filtering the data against bisquare-envelopedsine waves, in what amounts to an over-sampled wavelettransform. The filtering procedure yields a standardmatched filter signal to noise ratio (SNR), ρ, which isused to identify excess power events in each interferome-ter (quoted in terms of the quantity Z = ρ2/2). Triggersfrom the various interferometers are combined to givecandidate events if they have consistent central times andfrequencies. QPipeline also looks for coherence in the re-sponse of the H1 and H2 interferometers by comparingthe excess power of sums (the coherent combination H+)and differences (the null combination H−) of the data.Rather than using the single-interferometer H1, H2, L1,signal to noise ratios, the QPipeline analysis uses theSNRs in the transformed channels H+, H−, and L1. Adetailed description of the QPipeline algorithm can be

found in Appendix D.

Coherent WaveBurst (cWB) performs a time-frequency decomposition using critically sampled Meyerwavelets. The cWB version used in S5 replaces the sep-arate coincidence and correlation test (CorrPower) usedin the S4 analysis [17] by a single coherent search statis-tic based on a Gaussian likelihood function. Constrainedwaveform reconstruction is used to compute the networklikelihood and a coherent network amplitude. This coher-ent analysis has the advantage that it is not limited bythe performance of the least sensitive detector in the net-work. In the cWB analysis, various signal combinationsare used to measure the signal consistency among dif-ferent sites: a network correlation statistic cc , networkenergy disbalance ΛNET, H1-H2 disbalance ΛHH and apenalty factor Pf . These quantities are used in concertwith the coherent network amplitude η to develop effi-cient selection cuts. It is worth noting that the versionof cWB used in the S5 search is more advanced than theone used on LIGO and GEO data in S4 [18]. A detaileddescription of the cWB algorithm can be found in Ap-pendix E.

Both QPipeline and coherent WaveBurst use the free-dom to form linear combinations of the data to construct“null streams” that are insensitive to GWs. These nullstreams provide a powerful tool for distinguishing be-tween genuine GW signals and instrument artifacts [29].

VI. BACKGROUND AND TUNING

As mentioned in Sec. IV, the statistical properties ofthe noise triggers (background) are studied for all net-work combinations by analyzing time-shifted data, whilethe detection capabilities of the search pipelines for var-ious types of GW signals are studied by analyzing simu-lated signals (described in the following section) injectedinto actual detector noise. Plots of the parameters fornoise triggers and signal injections are then examinedto tune the searches. Thresholds on the parameters arechosen to maximize the efficiency in detecting GWs for apredetermined, conservative false alarm rate of roughly5 events for every 100 time shifts of the full data set.

For a given energy threshold, all three pipelines ob-served a much larger rate of triggers with frequenciesbelow 200 Hz than at higher frequencies. Therefore, eachpipeline set separate thresholds for triggers above andbelow 200 Hz, maintaining good sensitivity for higher-frequency signals at the expense of some sensitivity forlow-frequency signals. The thresholds were tuned sepa-rately for each detector network, and the cWB pipelinealso distinguished among a few distinct epochs with dif-ferent noise properties during the run. A more detaileddescription of the tuning process can be found in Appen-dices C, D, and E.

8

VII. SIMULATED SIGNALS AND EFFICIENCYCURVES

In this section we present the efficiencies of the differentalgorithms in detecting simulated GWs. As in previousscience runs, we do not attempt to survey the completespectrum of astrophysically motivated signals. Instead,we use a limited number of ad hoc waveforms that probethe range of frequencies of interest, different signal dura-tions, and different GW polarizations.

We choose three families of waveforms: sine-Gaussians,Gaussians, and “white noise bursts”. An isotropic skydistribution was generated in all cases. The Gaussianand sine-Gaussian signals have a uniformly distributedrandom linear polarization, while the white noise burstscontain approximately equal power in both polarizations.We define the amplitude of an injection in terms of thetotal signal energy at the Earth observable by an idealoptimally oriented detector able to independently mea-sure both signal polarizations:

h2rss =

∫ +∞

−∞(|h+(t)|2 + |h×(t)|2) dt (7.1)

=∫ +∞

−∞(|h+(f)|2 + |h×(f)|2) df.

In reality, the signal observed at an individual detec-tor depends on the direction Ω to the source and thepolarization angle Ψ through “antenna factors” F+ andF×:

hdet = F+(Ω,Ψ)h+ + F×(Ω,Ψ)h× . (7.2)

In order to estimate the detection efficiency as a func-tion of signal strength, the simulated signals were in-jected at 22 logarithmically spaced values of hrss rangingfrom 1.3× 10−22 Hz−1/2 to 1.8× 10−19 Hz−1/2 , steppingby factors of ∼

√2. Injections were performed at quasi-

random times regardless of data quality or detector state,with an average rate of one injection every 100 seconds.The efficiency of a method is then defined as the frac-tion of waveforms that are detected out of all that wereinjected into the data analyzed by the method.

A. Simulated signals

The first family of injected signals are sine-Gaussians.These are sinusoids with a central frequency f0, dimen-sionless width Q and arrival time t0, defined by:

h+(t0 + t) = h0 sin(2πf0t) exp[−(2πf0t)2/2Q2]. (7.3)

More specifically f0 was chosen to be one of (70, 100,153, 235, 361, 554, 849, 945, 1053, 1172, 1304, 1451,1615, 1797, 2000) Hz; and Q to be one of 3, 9, or 100.

The second family consists of Gaussian pulses de-scribed by the following expression:

h+(t0 + t) = h0 exp(−t2/τ2) (7.4)

where τ is chosen to be one of (0.05, 0.1, 0.25, 0.5, 1.0,2.5, 4.0, 6.0, 8.0) ms.

The third family are the “white noise bursts” (WNBs).These were generated by bandpassing white noise in fre-quency bands starting at 100 Hz, 250 Hz, or 1000 Hz, withbandwidth 10 Hz, 100 Hz, or 1000 Hz, and by time win-dowing with Gaussian profiles of duration (half of theinterval between the inflection points) equal to 100 ms,10 ms, or 1 ms. For each waveform type (a choice of cen-tral frequency, bandwidth, and duration), 30 waveformfiles with random data content were created. The injec-tions for each waveform type use random pairs selectedfrom the 30 created waveforms for the h+ and h× polar-izations (the selection avoids pairs with identical wave-forms). This results in unpolarized injections with equalamounts of power on average in each polarization state.

Each efficiency curve, consisting of the efficiencies de-termined for a given signal morphology at each of the 22hrss values, was fitted with an empirical four-parameterfunction. The efficiency curves for the logical OR combi-nation of the three pipelines and for the combined H1H2and H1H2L1 networks are shown for selected waveformsin Figs. 3 and 4. The hrss values yielding 50% detec-tion efficiency, h50%

rss , are shown in Tables I and II forsine-Gaussians with Q = 9 and for white noise bursts in-jected and analyzed in H1H2L1 data. The study of theefficiency for all the waveforms shows that the combina-tion of the methods is slightly more sensitive than thebest performing one, which is QPipeline for some of thesine-Gaussians, and cWB for all other waveforms consid-ered.

VIII. STATISTICAL AND CALIBRATIONERRORS

The h50%rss values presented in this paper have been ad-

justed to conservatively reflect systematic and statisticaluncertainties. The dominant source of systematic uncer-tainty is from the amplitude measurements in the fre-quency domain calibration. The individual amplitudeuncertainties from each interferometer can be combinedinto a single uncertainty by calculating a combined root-sum-square amplitude SNR and propagating the individ-ual uncertainties assuming each error is independent. Inaddition, there is a small uncertainty (about 1%) intro-duced by converting from the frequency domain to thetime domain strain series on which the analysis was actu-ally run. There is also phase uncertainty on the order of afew degrees in each interferometer, arising both from theinitial frequency domain calibration and the conversionto the time domain. However, this is not a significantconcern since the phase uncertainties at all frequenciescorrespond to phase shifts on the order of less than halfa sample duration. We therefore do not make any ad-justment to the overall systematic uncertainties due tophase error. Finally, statistical uncertainties on the fitparameters (arising from the binomial errors on the effi-

9

f (Hz) Q Combined cWB BN QP

70 9 25.8 25.9 227.4 33.1

100 9 10.3 10.5 13.6 14.0

153 9 6.3 6.5 7.8 8.8

235 9 6.0 6.3 7.7 6.8

361 9 10.9 11.2 16.3 12.0

554 9 12.0 12.6 15.5 12.9

849 9 18.1 19.0 23.7 19.2

945 9 20.6 21.6 27.8 22.2

1053 9 23.3 24.8 33.4 24.1

1172 9 25.2 26.8 36.5 26.3

1304 9 28.7 30.9 40.8 29.5

1451 9 32.0 35.0 48.1 32.9

1615 9 35.2 38.2 51.5 36.3

1797 9 42.0 44.2 62.2 45.4

2000 9 54.5 55.9 77.6 68.8

TABLE I: hrss values yielding 50% detection efficiency, inunits of 10−22 Hz−1/2, for different sine-Gaussian waveformsand pipelines in the H1H2L1 network. The first column isthe central frequency, the second the quality factor, the thirdthe h50%

rss of the logical OR of the pipelines, and the remain-ing three columns the h50%

rss of the individual pipelines. Theseh50%

rss values include an adjustment of 11.1% to take into ac-count calibration and statistical uncertainties as explained inSec. VIII.

f (Hz) BW (Hz) d (ms) Combined cWB BN QP

1000 1000 0.001 32.0 34.4 51.8 33.2

1000 1000 0.01 38.6 39.1 47.1 51.9

1000 1000 0.1 63.4 65.8 73.0 113.6

1000 100 0.01 22.2 22.6 30.9 25.9

1000 100 0.1 28.5 28.5 44.6 44.6

1000 10 0.1 21.5 21.4 30.8 44.8

100 100 0.01 6.5 6.7 7.5 9.2

100 100 0.1 7.9 7.9 9.9 14.1

100 10 0.1 9.1 9.1 13.7 12.7

250 100 0.01 7.3 7.6 18.6 8.5

250 100 0.1 8.8 8.9 11.6 13.4

250 10 0.1 5.9 5.9 9.0 17.6

TABLE II: hrss values yielding 50% detection efficiency, inunits of 10−22 Hz−1/2, for different white noise burst wave-forms and pipelines in the H1H2L1 network. The first col-umn is the central frequency, the second the bandwidth, thethird the duration of the gaussian window, the fourth theh50%

rss of the logical OR of the pipelines, and the remainingthree columns the h50%

rss of the individual pipelines. Theseh50%

rss values include an adjustment of 11.1% to take into ac-count calibration and statistical uncertainties as explained inSec. VIII.

(a)

]Hz [strain/rssh

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FIG. 3: Combined efficiencies of the three pipelines and twonetworks (H1H2L1 and H1H2) used in the upper limit analysisfor selected sine-Gaussian waveforms with (a) Q = 3, (b)Q = 9, (c) Q = 100. These efficiencies have been calculatedusing the logical OR of the pipelines and networks for thesubset of simulated signals that were injected in time intervalsthat were actually analyzed, and thus approach unity for largeamplitudes.

ciency measurements) affect h50%rss by approximately 1.4%

on average and are not much different for any particularwaveform.

The frequency-domain amplitude uncertainties areadded in quadrature with the other smaller uncertain-ties to obtain a total 1-sigma relative error for the SNR.The relative error in the hrss is then the same as the rel-ative error in the SNR. Thus, we adjust our sensitivityestimates by increasing the h50%

rss values by the reported

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250−260 Hz,0.1 s

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1000−2000 Hz,0.001 s

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1000−2000 Hz,0.1 s

FIG. 4: Combined efficiency of the three pipelines and twonetworks (H1H2L1 and H1H2) used in the upper limit analysisfor (a) selected linearly-polarized Gaussian waveforms; (b) se-lected band-limited white-noise bursts with two independentpolarization components. These efficiencies have been calcu-lated using the logical OR of the pipelines and networks forthe subset of simulated signals that were injected in time in-tervals that were actually analyzed, and thus approach unityfor large amplitudes.

percent uncertainties multiplied by 1.28 (to rescale froma 1-sigma fluctuation to a 90% confidence level upperlimit, assuming Gaussian behavior), which amounts to11.1% in the frequency band explored in this paper.

IX. SEARCH RESULTS

Once category 2 DQFs have been applied on the trig-gers produced from the unshifted (i.e. candidate sample)and time-shifted (background) data, histograms of thetwo populations are generated for each pipeline, inter-ferometer network and frequency band. See for exampletrigger distributions for the H1H2L1 network in Figs. 5,6, and 7. No unshifted triggers are found above thresholdin the final sample for any of the three pipelines and fournetwork configurations. We therefore have no candidateGW signals, and no follow up for possible detections isperformed. We proceed to set upper limits on the rate ofspecific classes of GWs.

2 3 4 5 6 7

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s

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100

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s

η

FIG. 5: Distributions of cWB H1H2L1 triggers after category2 DQFs were applied. Overlaid histograms for η for unshiftedtriggers (dots) and mean background estimated from time-shifted triggers (stair-step curve). The narrow error bars in-dicate the statistical uncertainty of the background estimate,while the shaded band indicates the expected root-mean-square statistical fluctuations on the number of backgroundtriggers in each bin. The top panel represents the triggerswith central frequency below 200 Hz while the bottom panelrepresents the triggers with central frequency above 200 Hz.

A. Upper limits

Our measurements consist of the list of triggers de-tected by each analysis pipeline (BN, QP, cWB) in eachnetwork data set (H1H2L1, H1H2, H1L1, H2L1). BNanalyzed the H1H2L1 data, QP analyzed H1H2L1 andH1H2, and cWB analyzed all four data sets. In general,the contribution to the upper limit due to a given pipelineand data set increases with both the detection efficiencyof the pipeline and the livetime of the data set. Since theduty cycle of the H1L1 and H2L1 data sets is small (2.4%and 4.5% after category 3 DQFs and category 3 vetoes,vs. 37.2% and 22.5% in H1H2L1 and H1H2), and thedata quality not as good, we decided a priori to not in-clude these data sets in the upper limit calculation. Weare therefore left with 5 analysis pipeline results: BN-H1H2L1, QP-H1H2L1, QP-H1H2, cWB-H1H2L1, andcWB-H1H2. We wish to combine these 5 results to pro-duce a single upper limit on the rate of GW bursts ofeach of the morphologies tested.

11

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FIG. 6: QPipeline triggers after category 2 DQFs were ap-plied. Overlaid histograms for H1H2 correlated energy for un-shifted H1H2 triggers (dots) and mean background estimatedfrom time-shifted triggers (stair-step curve). The narrow er-ror bars indicate the statistical uncertainty of the backgroundestimate, while the shaded band indicates the expected root-mean-square statistical fluctuations on the number of back-ground triggers in each bin. The top panel represents thetriggers with central frequency below 200 Hz while the bot-tom panel represents the triggers with central frequency above200 Hz.

We use the approach described in [30] to combine theresults of the different search detection algorithms andnetworks. Here we give only a brief summary of the tech-nique.

The procedure given in [30] is to combine the sets oftriggers according to which pipeline(s) and/or networkdetected any given trigger. For example, in the case oftwo pipelines “A” and “B”, the outcome of the countingexperiment is the set of three numbers ~n = (nA, nB, nAB),where nA is the number of events detected by pipeline Abut not by B, nB is the number detected by B but notby A, and nAB is the number detected by both. (Theextension to an arbitrary number of pipelines and datasets is straightforward.) Similarly, one characterizes thesensitivity of the experiment by the probability that anygiven GW burst will be detected by a given combinationof pipelines. We therefore compute the efficiencies ~ε =(εA, εB, εAB), where εA is the fraction of GW injectionsthat are detected by pipeline A but not by B, etc.

FIG. 7: BlockNormal triggers after category 2 DQFs were ap-plied. Overlaid histograms for Γ for unshifted H1H2L1 trig-gers (dots) and mean background estimated from time-shiftedtriggers (stair-step curve). The narrow error bars indicate thestatistical uncertainty of the background estimate, while theshaded band indicates the expected root-mean-square statis-tical fluctuations on the number of background triggers ineach bin. The top panel represents the triggers with centralfrequency below 200 Hz while the bottom panel represents thetriggers with central frequency above 200 Hz.

To set an upper limit, one must decide a priori how torank all possible observations, so as to determine whethera given observation ~n contains “more” or “fewer” eventsthan some other observation ~n′. Denote the ranking func-tion by ζ(~n). Once this choice is made, the actual set ofunshifted events is observed, giving ~n, and the rate upperlimit Rα at confidence level α is given by

1− α =∑

~N |ζ( ~N)≤ζ(~n)

P ( ~N |~ε,Rα ~T ) . (9.1)

Here P ( ~N |~ε,Rα ~T ) is the prior probability of observing~N given the true GW rate Rα, the vector containing thelivetimes of different data sets ~T (this is a scalar if we arecombining results of methods analyzing the same live-time), and the detection efficiencies ~ε. The sum is takenover all ~N for which ζ( ~N) ≤ ζ(~n); i.e., over all possibleoutcomes ~N that result in “as few or fewer” events thanwere actually observed.

12

As shown in [30], a convenient choice for the rank or-dering is

ζ(~n) = ~ε · ~n . (9.2)

That is, we weight the individual measurements(nA, nB, nAB, . . .) proportionally to the corresponding ef-ficiency (εA, εB, εAB, . . .). This simple procedure yields asingle upper limit from the multiple measurements. Fromthe practical point of view, it has the useful propertiesthat the pipelines need not be independent, and thatcombinations of pipelines and data sets in which it is lesslikely for a signal to appear (relatively low εi) are natu-rally given less weight.

Note that for the purpose of computing the upper limiton the GW, we are ignoring any background. This leadsto our limits being somewhat conservative, since a non-zero background contribution to ~n will tend to increasethe estimated limit.

In the present search, no events were detected by anyanalysis pipeline, so ~n = ~0. As shown in [30], in thiscase the efficiency weighted upper limit procedure givenby Eqs. (9.1) and (9.2) gives a particularly simple result:the procedure is equivalent to taking the logical OR of allfive pipeline/network samples. The α = 90% confidencelevel upper limit for zero observed events, R90%, is givenby

0.1 = exp(−εtotR90%T ) (9.3)

⇒ R90% =2.30εtotT

, (9.4)

where εtot is the weighted average of all the efficiencies(the weight is the relative livetime) and T is the totalobservation time. Fig. 8 shows the combined rate up-per limits as a function of amplitude for selected sine-Gaussian and Gaussian GW bursts. In the limit of strongsignals, εtotT goes to 224.0 days which is the union ofall time analyzed for the H1H2L1 and H1H2 networksafter category 3 DQFs. The rate limit thus becomes0.0098 day−1 = 3.6 yr−1.

X. SUMMARY AND DISCUSSION

The search for unmodeled GW bursts reported in thispaper is currently the most sensitive ever performed. Thequality of the data and the sensitivity of the data anal-ysis algorithms have improved since the S4 run, and thequantity of data available for analysis has increased bymore than an order of magnitude. These improvementsare reflected in the greater strain sensitivity (with hrss50%

values as low as ∼ 6×10−22 Hz−1/2) and the tighter limiton the rate of bursts (less than 3.6 events per year at90% confidence level) with large enough amplitudes tobe detected reliably. The most sensitive previous search,using LIGO S4 data, achieved hrss50% sensitivites as lowas a few times 10−21 Hz−1/2 and a rate limit of 55 eventsper year. We note that the IGEC network of resonant

FIG. 8: Selected exclusion diagrams showing the 90% con-fidence rate limit as a function of signal amplitude for Q=9sine-Gaussian (top) and Gaussian (bottom) waveforms for theresults in this paper (S5) compared to the results reportedpreviously (S1, S2, and S4).

bar detectors has set a more stringent rate limit, 1.5events per year at 95% confidence level [31], for GWbursts near the resonant frequencies of the bars withhrss >∼ 8×10−19 Hz−1/2 (see Sec. X of [14] for the detailsof this comparison).

In order to set an astrophysical scale to the sensitiv-ity achieved by this search, we now repeat the analysisand the examples presented for S4. Specifically, we canestimate what amount of mass converted into GW burstenergy at a given distance would be strong enough tobe detected by the search with 50% efficiency. Follow-ing the same steps as in [17], assuming isotropic emis-sion and a distance of 10 kpc we find that a 153 Hz sine-Gaussian with Q = 9 would need 1.7×10−8 solar masses,while for S4 the figure was 10−7M. For a source in theVirgo galaxy cluster, approximately 16 Mpc away, thesame hrss would be produced by an energy emission ofroughly 0.044Mc2, while for S4 it was 0.25Mc2.

We can also update our estimates for the detectabil-ity of two classes of astrophysical sources: core col-lapse supernovae and binary black-hole mergers. Weconsider first the core collapse supernova simulations byOtt. et al. [9]. In this paper gravitational waveformswere computed for three progenitor models: s11WW,m15b6 and s25WW. From S4 to S5 the astrophysicalreach for the s11WW and m15b6 models improved fromapproximately 0.2 to 0.6 kpc while for s25WW it im-

13

proved from 8 to 24 kpc. Second, we consider the bi-nary black hole merger calculated by the Goddard nu-merical relativity group [7]. A binary system of two 10-solar-mass black holes (total 20M) would be detectablewith 50% efficiency at a distance of roughly 4 Mpc com-pared to 1.4 Mpc in S4, while a system with total mass100M would be detectable out to ∼180 Mpc, comparedto ∼60 Mpc in S4. In each case the astrophysical reachhas improved by approximately a factor of 3 from S4 toS5.

At present, the analysis of the second year of S5 is wellunderway, including a joint analysis of data from Virgo’sVSR1 run which overlaps with the final 4.5 months of S5.Along with the potential for better sky coverage, posi-tion reconstruction and glitch rejection, the joint analysisbrings with it new challenges and opportunities. Look-ing further ahead, the sixth LIGO science run and sec-ond Virgo science run are scheduled to start in mid 2009,with the two LIGO 4 km interferometers operating in an“enhanced” configuration that is aimed at delivering ap-proximately a factor of two improvement in sensitivity,and comparable improvements for Virgo. Thus we willsoon be able to search for GW bursts farther out into theuniverse.

Acknowledgments

The authors gratefully acknowledge the support of theUnited States National Science Foundation for the con-struction and operation of the LIGO Laboratory andthe Science and Technology Facilities Council of theUnited Kingdom, the Max-Planck-Society, and the Stateof Niedersachsen in Germany for support of the construc-tion and operation of the GEO600 detector. The authorsalso gratefully acknowledge the support of the researchby these agencies and by the Australian Research Coun-cil, the Council of Scientific and Industrial Research ofIndia, the Istituto Nazionale di Fisica Nucleare of Italy,the Spanish Ministerio de Educacion y Ciencia, the Con-selleria d’Economia Hisenda i Innovacio of the Govern deles Illes Balears, the Royal Society, the Scottish Fund-ing Council, the Scottish Universities Physics Alliance,The National Aeronautics and Space Administration, theCarnegie Trust, the Leverhulme Trust, the David and Lu-cile Packard Foundation, the Research Corporation, andthe Alfred P. Sloan Foundation.

This document has been assigned LIGO Laboratorydocument number LIGO-P080056-v12.

APPENDIX A: DATA QUALITY FLAGS

Data quality flags are defined by the LIGO DetectorCharacterization group by carefully processing informa-tion on the behavior of the instrument. Some are definedonline, as the data are acquired, while others are formu-lated offline. A wide range of DQFs have been defined.

The relevance of each available DQF has been evaluatedand classified into categories which are used differentlyin the analysis, which we now describe.

Category 1 DQFs are used to define the data set pro-cessed by the search algorithms. They include out-of-science mode, the 30 seconds before loss of lock, periodswhen the data are corrupted and periods when test sig-nals are injected into the detector. They also includeshort transients that are loud enough to significantly dis-tort the detector response and could affect the powerspectral density used for normalization by the search al-gorithm, such as dropouts in the calibration and photo-diode saturations.

Category 2 flags are unconditional post-processingdata cuts, used to define the “full” data set used to lookfor detection candidates. The flags are associated withunambiguous malfunctioning with a proven correlationwith loud transients in the GW channel, where we under-stand the physical coupling mechanism. They typicallyonly introduce a fraction of a percent of deadtime overthe run. Examples include saturations in the alignmentcontrol system, glitches in the power mains, time-domaincalibration anomalies, and large glitches in the thermalcompensation system.

Category 3 DQFs are applied to define the “clean” dataset, used to set an upper limit in the absence of a detec-tion candidate. Any detection candidate found at a timemarked with a category 3 DQF would not be immediatelyrejected but would be considered cautiously, with specialattention to the effect of the flagged condition on detec-tion confidence. DQF correlations with transients in theGW channels are established at the single interferome-ter level. Examples include the 120 s prior to lock-loss,noise in power mains, transient drops in the intensity ofthe light stored in the arm cavities, times when one Han-ford instrument is unlocked and may negatively affectthe other instrument, times with particularly poor sensi-tivity, and times associated with severe seismic activity,high wind speed, or hurricanes. These flags introduce upto ∼10% dead time.

Category 4 flags are advisory only: We have no clearevidence of a correlation to loud transients in the GWchannel, but if we find a detection candidate at thesetimes, we need to exert caution. Examples are certaindata validation issues and various local events marked inthe electronic logs by operators and science monitors.

Figure 9 shows the fraction of KleineWelle triggers thatare eliminated by category 2 and 3 DQFs, respectively,in the L1 interferometer, as a function of the significanceof the energy excess identified by the trigger, which isevaluated assuming stationary, random noise. To ensureDQFs are independent of the presence of a true GW, weverified they are not triggered by hardware injections.

14

FIG. 9: The two examples in the figure show the fraction ofsingle interferometer (L1) KleineWelle triggers eliminated bycategory 2 (top) and category 3 (bottom) DQFs, as a functionof a threshold on the significance. The cumulative impact onthe lifetime is less then 7 percent (mostly from category 3DQFs), and the cuts are most effective for the loudest triggers.For example, a significance of 1000 means that if the detectornoise were Gaussian, the noise would have a probability e−1000

of fluctuating to produce such a loud trigger.

APPENDIX B: EVENT-BY-EVENT VETOES

Event-by-event vetoes attempt to discard GW channelnoise events by using information from the many envi-ronmental and interferometric auxiliary channels whichmeasure non-GW degrees of freedom. Good vetoes arefound by looking for situations in which a short (∼ms)noise transient in an auxiliary channel, identified by theKleineWelle (KW) algorithm, often coincides within ashort interval (∼100 ms) with noise transients in the GWchannel. The work, then, is in identifying useful auxiliarychannels which are well correlated with noise transientsin the GW data, choosing the relevant veto parametersto use, and finally establishing that the veto procedurewill not systematically throw out true GWs.

The trigger properties used for veto studies are the KWsignal energy-weighted central time and the KW statis-tical significance. The correlation between noise eventsin the GW channel and an auxiliary channel is deter-mined by a comparison of the coincidence rate measuredproperly and coincidence rate formed when one of thetime series has been artificially time-shifted with respectto the other. Alternatively, we can compare the num-ber of coincidences with the number expected by chance,assuming Poisson statistics.

As for the DQFs, category 2 vetoes are defined us-ing only a few subsets of related channels, showing the

more obvious kinds of mechanisms for disturbing the in-terferometers – either vibrational or magnetic coupling.Furthermore, for this S5 analysis we insist that multiple(3 or more) channels from each subset be excited in coin-cidence before declaring a category 2 veto, to ensure thata genuine disturbance is being measured in each case. Bycontrast, the category 3 vetoes use a substantially largerlist of channels. The aim of this latter category of vetois to produce the optimum reduction of false events for achosen tolerable amount of livetime loss.

a. Veto effectiveness metrics

Veto efficiency is defined for a given set of triggers asthe fraction vetoed by our method. We use a simpleveto logic where an event is vetoed if its peak time fallswithin a veto window, and define the veto dead-time frac-tion to be the fraction of livetime flagged by all the vetowindows. Assuming that real events are randomly dis-tributed in time, dead-time fraction represents the proba-bility of vetoing a true GW event by chance. We will referto the flagged dead-time as the veto segments. A veto ef-ficiency greater than the dead-time fraction indicates acorrelation between the triggers and veto segments.

Under either the assumption of randomly distributedtriggers, or randomly distributed dead-time, the numberof events that fall within the flagged dead-time is Pois-son distributed with mean value equal to the number ofevents times the fractional dead-time, or equivalently, theevent rate times the duration of veto segments. We de-fine the statistical significance of actually observing Nvetoed events as S(N) = − log [PPoiss(x ≥ N)].

We must also consider the safety of a veto condition:auxiliary channels (besides the GW channel) could inprinciple be affected by a GW, and a veto condition de-rived from such a channel could systematically reject agenuine signal. Hardware signal injections imitating thepassage of GWs through our detectors, performed at sev-eral pre-determined times during the run, have been usedto establish under what conditions each channel is safeto use as a veto. Non-detection of a hardware injectionby an auxiliary channel suggests the unconditional safetyof this channel as a veto in the search, assuming that areasonably broad selection of signal strengths and fre-quencies were injected. But even if hardware injectionsare seen in the auxiliary channels, conditions can readilybe derived under which no triggers caused by the hard-ware injections are used as vetoes. This involves imposingconditions on the strength of the triggers and/or on theratio of the signal strength seen in the auxiliary channelto that seen in the GW channel.

Veto safety was quantified in terms of the probabilityof observing ≥N coincidence events between the auxil-iary channel and hardware injections vs. the number ofcoincidences expected from time-shifts.

The observed concident rate is a random variableitself that fluctuates around the true coincident rate.

15

In the veto analysis we use the 90% confidence upperlimit on the background coincidence rate which canbe derived from the observed coincidence rate. Thisprocedure makes it easier to consider a veto safe thanunsafe and the reason for this approach was to leantoward vetoing questionable events. A total of 20time-shifts were performed. The analysis looped over7 different auxiliary channel thresholds and calculatedthis probability, and a probability of less than 10%caused a veto channel at and below the given thresholdto be judged unsafe. A fixed 100 ms window betweenthe peak time of the injection and the peak time ofthe KleineWelle trigger in the auxiliary channel was used.

All channels used for category 2 vetoes were found tobe safe at any threshold. Thresholds for category 3 vetochannels were chosen so as to ensure that the channelwas safe at that threshold and above.

b. Selection of veto conditions

For the purpose of defining conservative vetoes ap-propriate for applying as category 2 (before looking forGW detections), we studied environmental channels. Wefound that these fall into groups of channels that eachveto a large number of the same events. Based on thisobservation, three classes of environmental channels wereadopted as vetoes. For LHO these classes were 24 mag-netometers and voltmeters with a KW threshold of 200and time window of 100 ms, and 32 accelerometers andseismometers with a threshold on the KW significance of100 and a time window of 200 ms. For LLO these were12 magnetometers and voltmeters with a KW thresholdof 200 and a time window of 100 ms. We used all of thechannels that should have been sensitive to similar effectsacross a site, with the exception that channels known tohave been malfunctioning during the time period wereremoved from the list.

To ensure that our vetoes are based on true environ-mental disturbances, a further step of voting was imple-mented. An event must be vetoed by three or morechannels in a particular veto group in order to be dis-carded from the detection search. These conditions re-move ∼0.1% from the S5 livetime.

In the more aggressive category 3 vetoes, used forcleaning up the data for an upper limit analysis, we drawfrom a large number of channels (about 60 interferomet-ric channels per instrument, and 100 environmental chan-nels per site). This task is complicated by the desire tochoose optimal veto thresholds and windows, and the factthat the veto channels themselves can be highly corre-lated with each other so that applying one veto channelchanges the incremental cost (in additional dead-time)and benefit (in additional veto efficiency) of applying an-other. Applying all vetoes which perform well by them-selves often leads to an inefficient use of dead-time asdead-time continues to accumulate while the same noise

events are vetoed over and over.For a particular set of GW channel noise events, we

adopt a “hierarchical” approach to choose the best sub-set of all possible veto conditions to use for a target dead-time. This amounts to finding an ordering of veto condi-tions (veto channel, threshold, and window) from best toworst such that the desired set of veto conditions can bemade by accumulating from the top veto conditions solong as the dead-time does not exceed our limit, which istypically a few percent.

We begin with an approximately ordered list based onthe performance of each veto condition (channel, window,and threshold) considered separately. Incremental vetostatistics are calculated for the entire list of conditionsusing the available ordering. This means that for a givenveto condition, statistics are no longer calculated over theentire S5 livetime, but only over the fraction of livetimethat remains after all veto conditions earlier in the listhave been applied. The list is then re-sorted accordingto the incremental performance metric and the process isrepeated until further iterations yield a negligible changein ordering.

The ratio of incremental veto efficiency to incrementaldead-time is used as a performance metric to sort vetoconditions. This ratio gives the factor by which the rateof noise events inside the veto segments exceeds the aver-age rate. By adopting veto conditions with the largest in-cremental efficiency/dead-time ratio, we maximize totalefficiency for a target dead-time. We also set a thresholdof probability P < 0.001 on veto significance (not to beconfused with the significance of the triggers themselves).This is particularly important for low-number statisticswhen large efficiency/dead-time ratios can occasionallyresult from a perfectly random process.

Vetoes were optimized over several different sets of GWchannel noise events including low-threshold H1H2L1 co-herent WaveBurst time-shifted events, H1H2 coherentWaveBurst playground events, as well as QPipeline andKleineWelle single-interferometer triggers. For example,the effect of data quality flags and event-by-event vetoeson the sample of coherent WaveBurst time-shifted eventsis shown in Fig. 10. Our final list of veto segments toexclude from the S5 analysis is generated from the unionof these individually-tuned lists.

APPENDIX C: THE BLOCKNORMAL BURSTSEARCH ALGORITHM

1. Overview

The BlockNormal analysis pipeline follows a similarlogic to the S4 burst analysis [17] by looking for burststhat are both coincident and correlated. The BlockNor-mal pipeline uses a change-point analysis to identify co-incident transient events of high significance in each de-tector’s data. The subsequent waveform correlation testis the same as that used in the S4 analysis.

16

0.000 0.005 0.010 0.015 0.020 0.025 0.030

Fraction of livetime removed

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14F

racti

on

of

even

ts v

eto

ed

Hierarchical veto tuning on cWB events

4.5 5.0 5.5 6.0 6.5 7.0 7.5

Coherent network amplitude

0

10

20

30

40

50

60

Tim

e-s

hif

ted

even

ts

Data Quality and vetoes on cWB outliers

removed by Cat2 environmental vetoesremoved by Cat3 data quality flagsremoved by Cat3 hierarchical vetoessurviving all data quality and vetoes

FIG. 10: Top: Accumulated veto efficiency versus dead-timeas vetoes are applied cumulatively down the veto list. Thebest vetoes are applied first, so we see a general decrease inthe effectiveness of vetoes at higher dead-time. Vetoes fromenvironmental channels are artificially prioritized over inter-ferometric channels, giving rise to the knee in the plot around0.8% deadtime where the environmental vetoes are exhausted.Bottom: Histogram of coherent network amplitude, η, forcoherent WaveBurst time-shifted (background) events repre-senting 100 S5 livetimes. The different shades show eventsremoved by data quality cuts and vetoes at various stages inthe analysis.

A unique feature of the BlockNormal analysis is that itcan be run on uncalibrated time series data—neither thechange point analysis nor the correlation test are sensitiveto the overall normalization of the data.

2. Data conditioning

The BlockNormal search operated on the frequencyrange 80 to 2048 Hz. To avoid potential issues withthe additional processing and filtering used to create cal-ibrated data, and to be immune to corrections in thecalibration procedure, the analysis was run on the uncal-ibrated GW channel from the LIGO interferometers.

Lower Bound (Hz) Upper Bound (Hz) Bandwidth (Hz)

80 192 112

192 320 128

362 518 156

518 674 156

710 864 154

864 1018 154

1060 1212 152

1212 1364 152

1408 1558 150

1558 1708 150

1756 1902 146

1902 2048 146

TABLE III: Frequency Bands for BlockNormal Analysis

The data conditioning began with notch filters to sup-press out-of-band (below 80 Hz or above 2048 Hz) spec-tral features such as low-lying calibration lines, the strong60 Hz power-line feature and violin mode harmonics justabove 2048 Hz. The time-series data were then down-sampled to 4096 Hz to suppress high-frequency noise.The power-line harmonics in each band were removedusing Kalman filters [32, 33]. The large amount of powerat low frequencies in the uncalibrated GW channel wassuppressed with a highpass filter designed with the Parks-McClellan algorithm.

Because the BlockNormal method is purely a time-domain statistic, the interferometer data must be dividedinto frequency bands to achieve a degree of frequencyresolution on the bursts. For this analysis, 12 frequencybands approximately 150 Hz in bandwidth spanned therange from 80 Hz to 2048 Hz (see Table III). There aregaps between some bands to avoid the significant non-stationary noise from the violin modes of the mirror sus-pension wires.

The division into the twelve frequency bands was doneusing a basebanding procedure. Any calibration lineswithin the band were removed by low-order regressionfiltering against the calibration line injection channeldata. A final whitening filter of modest order was ap-plied in each band to satisfy the BlockNormal statistic’sassumption of Gaussianity in the background noise. Thedata conditioning procedures also had to minimize mix-ing noise characteristics between different time periodsfor the change-point analysis, and thus could not rely onpredictive filtering.

3. Change-point analysis

The BlockNormal algorithm uses a Bayesian statistictermed ρ2 to perform a change-point analysis using thenoise characteristics of time-series data. For an inter-val of N time-series samples x[k], this statistic measures

17

the statistical likelihood (at each sample k within thatinterval) that the data prior to that point are more con-sistent with a different Gaussian-distributed (or normal)noise source than are the data following that point. It isdefined as

ρ2,k = KρN

√π

2

[k−(k−1)/2(N − k)−(N−k−1)/2

N−(N−1)/2

](C1)

×

[Y−k/21,k Y

−(N−k)/2k+1,N

Y−N/21,N

] [Γ(k/2)Γ((N − k)/2)

Γ(N/2)

]where

Yi,j := x2i,j − xi,j

2 (C2)

xi,j :=1

j − i+ 1

j∑l=i

x[l] (C3)

x2i,j :=

1j − i+ 1

j∑l=i

x[l]2 . (C4)

The quantity Kρ is a constant proportional to βR/fs,where β is the prior probability, R the desired rate ofblocks, and fs the sample rate. In fact each intervalis searched for all change-points where ρ2,k exceeds athreshold value ρE , where ρE is implemented as a num-ber times Kρ. The sub-intervals between change-pointsare termed “blocks”. The statistical significance of eachsuch block is based on its “excess power” ξ∗ defined as

ξ∗ = N × (µ2 + ν)/(µ20 + ν0) ∼ χ2

N (C5)

where the block has mean µ and variance ν against abackground of mean µ0 and variance ν0. Events wereselected by requiring the negative-log-likelihood of ξ∗(termed ΛE) to exceed a threshold. Here

ΛE = −ln(Pr[ξ > ξ∗]) (C6)

where

Pr[ξ > ξ∗] = γ(N/2, ξ∗/2)/γ(N/2). (C7)

The variance-weighted time centroid, τ (2), of eachevent of n samples of amplitude xi and time ti was cal-culated:

τ (2) =∑ni=1 ti(xi − µ)2∑ni=1(xi − µ)2

=∑ni=1 ti(xi − µ)2

(n− 1)ν. (C8)

The calibrated band-limited strain energy of each eventwas estimated using the frequency-averaged responseR(f) over that band:

Ef = R(f)(µ2n+ ν(n− 1)) . (C9)

The BlockNormal algorithm was applied separately tothe data in each frequency band (Table III) to select can-didate GW burst events. The burst event generation wasdone on relatively long-duration epochs (up to 1200 s) of

continuous data to provide the best measure of the back-ground noise characteristics.

Prior to the network coincidence step, events withineach frequency band that are nearly adjacent were clus-tered into composite events. Then, events between ad-jacent frequency bands whose time centroids were closewere clustered into composite multiband events. Allevents were then characterized by their frequency cov-erage. For composite events, the effective time centroidwas the energy-weighted average of the time centroid ofthe constituent events. The band-limited energy for com-posite events was simply the sum of the per-event ener-gies. The central frequency for events in a single bandwas estimated by the average frequency of that band. Formulti-band events, the energy-weighted average of thesecentral frequencies was used.

4. Network coincidence

The signals from actual GW bursts in the LIGO inter-ferometers should be separated in time by no more thanthe maximum transit time (10 ms) for GW between theHanford and Livingston sites. For the co-located interfer-ometers at Hanford, there should be no time separation.The separation observed in the reconstructed events islarger due to limited time resolution, phase-delays in fil-tering, etc. For a candidate trigger, the time differencebetween candidate events in each pair of interferometers,|τ (2)i −τ

(2)j |, was required to fall within a fixed coincidence

window, ∆Tij , for that pair of interferometers. This coin-cidence window had to be much broader than the transittime to account for limited time resolution and skewing ofthe time distributions from differential antenna responseto h+ and h× waveforms.

The signals from actual GW bursts should also havesimilar strain amplitude (and hence statistical signifi-cance) in each interferometer. We derived a measure ofcoincident significance from the excess power significanceΛE in each candidate event in the trigger. This measuremust correct for the lower significance for GW signals inthe shorter H2 interferometer (as compared to the H1interferometer) as well as the fluctuation of the relativeGW signal strengths at the two LIGO sites due to mod-ulation from the antenna factors. The chosen metric forcoincident significance, termed “combined power” or PC,was defined as

PC = (ΛE,H1ΛE,H2ΛE,L1)1/3 . (C10)

This formulation was found to have the best performancein optimizing sensitivity to GW burst signals as a func-tion of the background trigger rate.

The coincidence procedure first identified events fromeach of the three detectors that had overlapping fre-quency coverage. These events then had to have timecentroids whose difference ∆T was less than 100 ms. Suchtime-coincidence events were retained as GW burst trig-

18

gers if their combined power PC was above a thresholdof 22.

5. Network correlation

The signals from GW bursts in each interferometer re-sult from the same parent waveforms, and thus shouldhave a large correlation sample-by-sample (after correc-tion for propagation delay). The cross-correlation statis-tic Γ reported by the CorrPower [34] package is the max-imum of the average correlation confidence of pair-wisecorrelation tests. It is positive-definite. Larger valuesdenote greater statistical certainty of coherence. TheCorrPower package was run on the list of candidate trig-ger times produced in the coincidence step. It retrievedthe full time-series data from each interferometer aroundthat time, calibrated the data, and calculated the Γ cross-correlation statistic. For the three LIGO interferometers,cuts were also made on the three pair-wise correlationtests.

Additional selection criteria took advantage of the spe-cial relationship for GW signals from the co-located in-terferometers H1 and H2. One was the signed correla-tion factor between the H1 and H2 interferometers fromthe CorrPower processing, termed R0. For triggers fromGW bursts, this correlation factor should be positive.For triggers from a background of random coincidences,there should be an equal number of positive and negativecorrelation factors. Also, since the H1 and H2 interfer-ometers receive the same GW signal, the ratio of hrss,H2

to hrss,H1 should be close to one for a true GW burst. Incontrast, for triggers from a random background this ra-tio will be centered around one-half. This arises becausethe H2 interferometer is approximately half as sensitiveas H1, so signals of the same statistical significance (nearthe threshold) will have only one-half the amplitude inH2 as they do in H1. To simplify thresholding, the ab-solute value of the logarithm of the ratio was calculatedRH1H2 = | log10(hrss,H1/hrss,H2)| for later use.

The choices of tuning parameters are described in Ta-ble IV. Figure 11 illustrates an example of plots used totune the figures of merit for the H1H2L1 network.

TABLE IV: Cuts used by the BlockNormal-CorrPowerpipeline in the first year of S5. The parameters are: combinedpower PC, overall CorrPower Γ value, CorrPower Γ values forvarious detector pairs, H1-H2 correlation R0, and estimatedhrss values in H1 and H2.

H1H2L1 Network

PC > 2

Γ > 5.0 for f < 200 Hz

Γ > 3.8 for f > 200 Hz

ΓH1H2 > 0.5, ΓH1L1 > 0.3, ΓH2L1 > 0.3

R0 > 0

| log10(hrss,H1/hrss,H2)| < 0.4

FIG. 11: Distribution of background and injection events withrespect to the CorrPower Γ. The narrow black histogramrepresents the background (noise) triggers while the broaderhistogram represents the distribution of the injections. Thesetriggers were generated in the H1H2L1 network and containfrequencies below 200 Hz. The vertical line indicates the cutmade on this quantity.

APPENDIX D: THE QPIPELINE BURSTSEARCH ALGORITHM

1. Overview

QPipeline is an analysis pipeline for the detection ofGW bursts in data from interferometric gravitationalwave detectors [25]. It is based on the Q transform [26], amulti-resolution time-frequency transform that projectsthe data under test onto the space of bisquare-windowedcomplex exponentials characterized by central time τ ,central frequency f0, and quality factor Q:

X(τ, f0, Q) =∫ +∞

−∞x(f)w(f, f0, Q)e+i2πfτdf , (D1)

where the bisquare window w(f, f0, Q) is

=

A

[1−

(fQ

f0

√5.5

)2]2

for f <f0

√5.5Q

0 otherwise

(D2)

with

A =(

315128√

5.5Q

f0

)1/2

. (D3)

The bisquare window is a close approximation to aGaussian window in frequency space; the QPipeline is ef-fectively a templated matched filter search [35] for signalsthat are Gaussian enveloped sinusoids in the whitenedsignal space.

19

2. Data conditioning

Before applying the Q transform, the data are firstwhitened by zero-phase linear predictive filtering [25, 36].In linear predictive whitening, the nth sample of a dis-crete data sequence is assumed to be well modeled by alinear combination of the previous M samples:

x[n] =M∑m=1

c[m]x[n−m] . (D4)

The resulting whitened data stream is the prediction er-ror sequence e[n] = x[n] − x[n] that remains after se-lecting the coefficients c[m] to minimize the error in theleast-squares sense.

The prediction error length M is taken to be equal tothe length of the longest basis function under test, whichis approximately 1 second. This ensures that the dataare uncorrelated on the time scales of the analysis.

In order to avoid introducing phase errors betweendetectors, a modified zero-phase whitening filter is con-structed by zero-padding the initial filter, converting tothe frequency domain, and discarding all phase informa-tion.

3. Measurement basis

The space of Gaussian enveloped complex exponen-tials is an over-complete basis of waveforms, whose du-ration σt and bandwidth σf have the minimum pos-sible time-frequency uncertainty, σtσf = 1/4π, whereQ = f0/

√2σf . As a result, they provide the tightest pos-

sible constraints on the time-frequency area of a signal,maximizing the measured signal to noise ratio (SNR) andminimizing the probability that false triggers are coinci-dent in time and frequency between multiple detectors.

In practice, the Q transform is evaluated only for afinite number of basis functions, which are more com-monly referred to as templates or tiles. These templatesare selected to cover a targeted region of signal space,and are spaced such that the fractional signal energy loss−δZ/Z due to the mismatch δτ , δf0, and δQ betweenan arbitrary basis function and the nearest measurementtemplate,

−δZZ' 2π2f2

0

Q2δτ2+

1 +Q2

2f20

δf20 +

12Q2

δQ2− 1f0Q

δf0 δQ,

(D5)is no larger than ∼20%. This naturally leads to a tilingof the signal space that is logarithmic in Q, logarithmicin frequency, and linear in time.

For this search, the QPipeline was applied to searchthe space of sinusoidal Gaussians with central frequencyfrom 48 Hz to 2048 Hz, and with Q from

√5.5 to 100/

√2.

4. Trigger generation

The statistical significance of Q transform projectionsare given by their normalized energy Z, defined as the ra-tio of squared projection magnitude to the mean squaredprojection magnitude of other templates with the samecentral frequency and Q. For the case of ideal whitenoise, Z is exponentially distributed and is related to thematched filter SNR quantity ρ [35] by the relation

Z = |X|2/〈|X|2〉τ = − ln Pr[Z ′ > Z] = ρ2/2 . (D6)

The Q transform is applied to the whitened data andnormalized energies are computed for each measurementtemplate as a function of time. Templates with statis-tically significant signal content are then identified byapplying a threshold on the normalized energy. Finally,since a single event may potentially produce multipleoverlapping triggers due to the overlap between measure-ment templates, only the most significant of overlappingtemplates are reported as triggers.

Clustering of nearby triggers is not used in evaluatingthe significance of events. As a result, the detectability ofGW burst signals depends on their maximum projectiononto the space of Gaussian enveloped sinusoids.

5. Coherence

For this search, the QPipeline took advantage of theco-located nature of the two LIGO Hanford detectors toform two linear combinations of the data streams fromthe two detectors. This coherent analysis makes use ofcorrelations in the data to distinguish true GW signalsfrom instrumental glitches.

a. Coherent signal stream

The first combination is the coherent signal stream,H+, a frequency dependent weighted sum of the datafrom the Hanford detectors which maximizes the effectiveSNR. The weighting is inversely proportional to the noisepower spectral density, S(f) :

xH+(f) =(

1SH1

+1SH2

)−1(xH1(f)SH1(f)

+xH2(f)SH2(f)

)(D7)

The resulting combination is treated as the output ofa new hybrid, “coherent” detector. Under the assump-tion that the power spectral density is approximately flatacross the window bandwidth, applying the Q transformto this data stream leads to a coherent energy value,|Xcoh

H+ |2, which takes the following form:

|XcohH+ |2 =

(1SH1

+ 1SH2

)−2

×(|XH1|2S2

H1+ |XH2|2

S2H2

+ X∗H1XH2+XH1X

∗H2

SH1SH2

)(D8)

20

where XH1, XH2, and XcohH+ are functions of τ , f0, and

Q, and the asterisk denotes complex conjugation. Thelast term represents the contribution of the cross-term,and is conceptually similar to a frequency domain rep-resentation of a cross-correlation of the H1 and H2 datastreams.

The energy expected in the coherent data stream ifthere were no correlations in the data can be character-ized by the “incoherent” terms in Eq. (D8):

|X incH+|2 =

(1SH1

+1SH2

)−2( |XH1|2

S2H1

+|XH2|2

S2H2

).

(D9)The coherent and incoherent energies can then be nor-malized in the manner of Eq. (D6):

ZcohH+ = |Xcoh

H+ |2/〈|XcohH+ |2〉τ (D10)

Z incH+ = |X inc

H+|2/〈|X incH+|2〉τ (D11)

The correlation between the detectors can then be mea-sured by the correlated energy, Zcorr

H+ , given by

ZcorrH+ = Zcoh

H+ − Z incH+ '

X∗H1XH2 +XH1X∗H2

SH1 + SH2. (D12)

b. Null stream

The second combination is the difference between thecalibrated data from the two detectors, known as the nullstream, and is defined as

xH−(f) = xH1(f)− xH2(f). (D13)

By subtracting the co-located streams, any true gravi-tational wave signal should be canceled. The resultingcombination is treated as the output of a new hybrid“H−” detector, which shows significant energy contentin the presence of instrumental glitches but does not re-spond to gravitational waves. Glitches are identified bythresholding on the corresponding normalized “null en-ergy”, Zcoh

H− , calculated in an analogous manner to ZcohH+ .

Signal tiles found to be in coincidence with significantnull stream tiles are vetoed as instrumental glitches, andare not considered as candidate events. The threshold onZcoh

H− can be expressed as

ZcohH− > α+ βZ inc

H− (D14)

where α is chosen to limit the veto rate in Gaussian noiseto ∼ 1 per 2048 tiles and β is a parameter correspondingto the allowed tolerance in calibration uncertainty. Thisis an energy factor, and corresponds to an amplitude cal-ibration uncertainty of approximately 22 percent.

We expect that highly energetic instrumental glitchescould leak energy into adjacent time-frequency bins, sothe veto coincidence requirement between signal and nullstreams is scaled to give more-significant null stream tilesmore area of veto influence in time-frequency space:

|τH− − τH+| < (δτ ′H− + δτH+)/2 , (D15)

|f0,H− − f0,H+| < (δf ′0,H− + δf0,H+)/2 (D16)

where τ and f0 are the central time and frequency of atile, δτ and δf are the duration and bandwidth of a tile,and the inflated null stream tile duration and bandwidthare defined as:

δτ ′H− = max(

1, 0.5√

2ZcohH−

)× δτH− , (D17)

δf ′0,H− = max(

1, 0.5√

2ZcohH−

)× δf0,H− (D18)

6. Coincidence

Coherent triggers from the two LIGO Hanford detec-tors were also tested for time-frequency coincidence withtriggers from the LIGO Livingston detector using the fol-lowing criteria, where T is the speed of light travel timeof 10 ms between the two LIGO sites:

|τH − τL| < max(δτH, δτL)/2 + T , (D19)

|f0,H − f0,L| < max(δf0,H, δf0,L)/2 . (D20)

Coincidence between the LIGO Hanford and Liv-ingston sites is not a requirement for detection, even ifdetectors at both sites are operational. The final trig-ger set is the union of triggers from the coherent H1H2trigger set and the coincident H1H2L1 trigger set. Theadditional requirement of coincidence permits a lowerthreshold, and therefore greater detection efficiency, forthe H1H2L1 data set.

The choices of tuning parameters are described in Ta-ble V. Figure 12 an example scatter plot used to tune thefigures of merit for the H1H2L1 network.

TABLE V: Cuts used by the QPipeline analysis in the firstyear of S5. The parameters are: H1/H2 coherent significanceZcoh

H+ , H1/H2 correlated significance ZcorrH+ , and L1 normalized

energy ZL1.

H1H2L1 Network

ZcohH+ > 20

ZcorrH+ > max

15, 50 4

r12.5

ZL1

!for f < 200 Hz

ZcorrH+ > max

5, 30

r12.5

ZL1

!for f > 200 Hz

ZL1 > 12.5

H1H2 Network

ZcohH+ > 20

ZcorrH+ > 50 for f < 200 Hz

ZcorrH+ > 30 for f > 200 Hz

21

FIG. 12: Scatter plot of the H1H2 correlated energy ZcorrH+ ,

[defined in Eq. (D12)], which measures the correlation of thestrain at the two Hanford interferometers, versus the L1 nor-malized energy [defined in Eq. (D6)]. The distribution of thebackground triggers is displayed in black while the distribu-tion of simulated GW signals in gray. This example tuningplot is for triggers generated for the H1H2L1 network andcontaining frequencies below 200 Hz. The cuts on these quan-tities are displayed on the plot as thick lines.

APPENDIX E: THE COHERENT WAVEBURSTSEARCH ALGORITHM

1. Overview

Coherent WaveBurst (cWB) is an analysis pipeline forthe detection and reconstruction of GW burst signalsfrom a network of detectors. The reconstructed gravi-tational waveform h that best describes the response ofthe network is used to compute the maximum likelihoodratio of the putative GW signal, which forms the maindetection statistic for the search. In effect, cWB is equiv-alent to a matched filter search with a very large templatebank representing all possible time-domain signals withshort duration.

The cWB pipeline is divided into three main stages:the generation of coherent triggers, the reconstruction ofthe GW signal and the computation of the maximumlikelihood ratio, and a post-production stage where addi-tional detection cuts are applied. By using weighted co-herent combinations of the data streams, cWB is not lim-ited by the least sensitive detector in the network. Thewaveform reconstruction allows various physical proper-ties of the signal to be estimated, including the sky loca-tion of the source. The coherent approach also allows forother statistics to be constructed, such as the null streamand coherent energy, to distinguish genuine GW signalsfrom environmental and instrumental artifacts.

2. Data conditioning and time-frequencydecomposition

The cWB analysis is performed in the wavelet domain.A discrete Meyer wavelet transformation is applied to thesampled detector output to produce a discrete waveletseries ak[i, j], where i is the time index, j is the scale in-dex and k is the detector index. An important propertyof Meyer wavelets is that they form an orthonormal ba-sis that allow for the construction of wavelet filters withsmall spectral leakage [27]. Wavelet series give a time-scale representation of data where each wavelet scale canbe associated with a certain frequency band of the initialtime series. Therefore a wavelet time-scale spectrum canbe displayed as a time-frequency (TF) scalogram, wherethe scale is replaced with the central frequency f of theband. The time series sampling rateR and the scale num-ber j determine the time resolution ∆tj(R) at this scale.The frequency resolution ∆fj is defined as 1/(2∆tj) anddetermines the data bandwidth at the scale j. The time-frequency resolution defines the tiling of the TF plane.The individual tiles (pixels) represent data samples in thewavelet domain. In the cWB pipeline a uniform tiling isused (∆fj(R) = R/2n, where n is the wavelet decompo-sition depth), which is obtained with the Meyer packettransformation [37]. In this case the TF resolution is thesame for all wavelet scales. For optimal localization ofthe GW energy in the TF plane, the cWB analysis isperformed at six different frequency resolutions: 8, 16,32, 64, 128 and 256 Hz.

Before the coherent analysis is performed, two dataconditioning algorithms are applied to the data in thewavelet domain: a linear prediction error (LPE) filter anda wavelet estimator of the power spectral density Sk[j].LPE filters are used to remove “predictable” componentsfrom an input data series. In the cWB pipeline theyare constructed individually for each wavelet layer andremove such components in the data as power line har-monics and violin-mode lines. A more detailed descrip-tion of the LPE filters can be found elsewhere [27, 38].The wavelet estimator of the one-sided power spectraldensity associated with each wavelet layer j is

Sk[j] = 2σ2k[j]R

(E1)

where σ2k[j] is the variance of the detector noise. In the

analysis we assume that the detector noise is Gaussianand quasi-stationary. The variance estimator may varywith time and therefore it is calculated for each samplein the wavelet layer: σ2

k[i, j]. The estimation of the noisevariance is performed on data segments of length 60 sec-onds, with 40 seconds overlap. Linear interpolation isused between two measurements to obtain σ2

k[i, j].

22

3. Coherent triggers

The first step in the analysis is to identify segments ofdata that may contain a signal. The triggers are evalu-ated using the whitened data vector w[i, j]

w[i, j](θ, φ) =(a1[i, j, τ1(θ, φ)]

σ1[i, j], ..,

aK [i, j, τK(θ, φ)]σK [i, j]

).

(E2)The sampled detector amplitudes in the wavelet domainak[i, j, , τk] take into account the time delays τk due tothe time-of-flight between the detectors, which in turndepend on the source coordinates θ and φ. Coherenttriggers are generated for the entire network by max-imizing the norm |w[i, j]| over the entire sky for eachtime-frequency location [i, j]. To do this, the sky is di-vided into square degree patches and the quantity |w| iscalculated for each patch from the delayed detector am-plitudes ak[i, j, τk]. By selecting clusters of pixels withthe maxθ,φ |w| above some threshold, one can identifycoherent triggers in the time-frequency plane. The datapixels wk[i, j] selected by this procedure are then used toreconstruct the GW signal and compute the maximumlikelihood statistic.

4. Maximum likelihood ratio functional

For the case of Gaussian quasi-stationary noise, thelikelihood that data a is purely instrumental noise is pro-portional to exp−(a|a)/2, while the likelihood that aGW signal h is present is proportional to exp−(a−h|a−h)/2. The ratio of these likelihoods can be used as adetection statistic. Here (x|y) defines a noise weightedinner product, which for K detectors with uncorrelatednoise can be written in the wavelet domain as

(x|y) =K∑k=1

∑i,j∈ΩT F

xk[i, j]yk[i, j]σ2k[i, j]

. (E3)

where time i and frequency j indices run over some time-frequency area ΩTF selected for the analysis. The co-herent WaveBurst pipeline defines L as twice the (log)likelihood ratio, and treats it as a functional in hdet(h)[38]:

L[h] = 2(a|hdet)− (hdet|hdet) , (E4)

where hkdet[i, j] are the detector responses (Eq. 7.2). Thenetwork sensitivity is characterized by the noise-scaledantenna pattern vectors f+ and f×:

f+(×)[i, j] =

(F1,+(×)(~Ω,Ψ)

σ1[i, j], ..,

FK,+(×)(~Ω,Ψ)σK [i, j]

).

(E5)Since the detector responses hkdet are independent of rota-tion by an arbitrary polarization angle in the wave frame,it is convenient to perform calculations in the dominant

polarization frame (DPF) [38]. In this frame the antennapattern vectors f+ and f× are orthogonal to each other:

(f+(ΨDPF ) · f×(ΨDPF )) = 0 (E6)

and we refer to them as f1 and f2 respectively. The corre-sponding solutions for the GW waveforms, h1 and h2, arefound by variation of the likelihood functional (Eq. (E4))that can be written as the sum of two terms, L = L1+L2,where

L1 =∑ΩT F

[2(w · f1)h1 − |f1|2h2

1

], (E7)

L2 =∑ΩT F

[2(w · f2)h2 − |f2|2h2

2

]. (E8)

The estimators of the GW waveforms for a particu-lar sky location are then the solutions of the equationsδL1/δh1 = 0 and δL2/δh2 = 0:

h1 = (w · f1)/|f1|2 , (E9)h2 = (w · f2)/|f2|2 . (E10)

Note, the norms |f1| and |f2| characterize the networksensitivity to the h1 and h2 polarizations respectively.The maximum likelihood ratio statistic for sky location(θ, φ) is calculated by substituting the solution for h intoL[h]. The result can be written as

Lmax(θ, φ) =K∑

n,m=1

Lmn =K∑

n,m=1

∑ΩT F

wnwmPnm ,

(E11)where the matrix P is the projection constructed fromthe components of the unit vectors e1 and e2 along thedirections of the f1 and f2 respectively:

Pnm = e1ne1m + e2ne2m . (E12)

The kernel of the projection P is the signal plane definedby these two vectors. The null space of the projection Pdefines the reconstructed detector noise which is referredto as the null stream.

The projection matrix is invariant with respect to therotation in the signal plane where any two orthogonalunit vectors can be used for construction of the Pnm.Therefore one can select vectors u and v such that (w ·v) = 0 and

Pnm = unum . (E13)

The unit vector u defines the vector

ξ = (w · u)u (E14)

whose components are estimators of the noise-scaled de-tector responses hkdet[i, j]/σk[i, j].

23

5. Regulators

In principle the likelihood approach outlined above canbe used for the reconstruction of the GW waveforms andcalculation of the maximum likelihood statistic. In prac-tice the formal solutions (E9), (E10) need to be regular-ized by constraints that account for the way the networkresponds to a generic GW signal [38]. For example, thenetwork may be insensitive to GW signals with a partic-ular sky location or polarization, resulting in an ill-posedinversion problem. These problems are addressed by us-ing regulators and sky-dependent penalty factors.

A classical example of a singular inversion problem is anetwork of aligned detectors where the detector responseshkdet are identical. In this case the algorithm can be con-strained to search for one unknown function rather thanfor the two GW polarizations h1 and h2, which span alarger parameter space. Note that in this case |f2| = 0,Eq. (E10) is ill-conditioned and the solution for the h2

waveform cannot be found. Regulators are importantnot only for aligned detectors, but also for networks ofmisaligned detectors, for example, the LIGO and Virgonetwork. Depending on the source location, the networkcan be much less sensitive to the second GW component(|f2|2 << |f1|2) and the h2 waveform may not be recon-structable from the noisy data.

In the coherent WaveBurst analysis we introduce a reg-ulator by modifying the norm of the f2 vector:

|f ′2|2 = |f2|2 + δ , (E15)

where δ is a tunable parameter. For example, if δ = ∞,the second GW component is entirely suppressed and theregulator corresponds to the “hard constraint” describedin Ref. [38]. In this case the unit vector u (see Eq. (E13))is pointing along the f+ direction. In the cWB analysisthe parameter δ is chosen to be

δ =(

0.01 +2|w|2

)∑k

1σ2k[i, j]

. (E16)

This regulator is more stringent for weak events whichare generated by the pipeline at much higher rate thanthe loud events.

The introduction of the regulator creates an obviousproblem for the construction of the projection matrix.Namely, the vector e′2 = f2/|f ′2| and the correspondingvector u′ obtained by rotation of e1 and e′2 in the signalplane are not unit vectors if δ 6= 0. To fix this problem were-normalize the vector u′ to unity and use it for calcula-tion of the maximum likelihood ratio and other coherentstatistics.

6. Coherent statistics

When the detector noise is Gaussian and stationary,the maximum likelihood Lmax is the only statistic re-quired for detection and selection of the GW events. In

this case the false alarm and the false dismissal proba-bilities are controlled by the threshold on Lmax which isan estimator of the total SNR detected by the network.However, the real data are contaminated with instrumen-tal and environmental artifacts and additional selectioncuts should be applied to separate them from genuineGW signals [27]. In the coherent WaveBurst methodthese selection cuts are based on coherent statistics con-structed from the elements of the likelihood and the nullmatrices. The diagonal terms of the matrix Lmn de-scribe the reconstructed normalized incoherent energy.The sum of the off-diagonal terms is the coherent energyEcoh detected by the network.

The next step is to optimize the solution over the sky.Often, depending on the network configuration, the re-construction of source coordinates is ambiguous. For ex-ample, for two separated detectors the relative time de-lay that yields maximum correlation between the datastreams corresponds to an annulus on the sky. In thiscase, an “optimal” source location is selected, where thereconstructed detector responses are the most consistentwith the output detector data streams. To properly ac-count for the directional sensitivity of the network theoptimization over sky locations has to be more than asimple maximization of Lmax(θ, φ). In the cWB analysisthe statistic that is maximized has the form

Lsky(θ, φ) = Lmax Pf cc, (E17)

where Pf is the penalty factor and cc is the network cor-relation coefficient. Pf and cc are defined below in termsof the matrix Lmn =

∑ΩT F

wnwmPnm and the diago-nal matrices Enm = Enδnm and Hnm = Hnδnm whichdescribe the normalized energy in the detectors, and thenormalized reconstructed signal energy (see Eq. (E14)),with

Ek =∑ΩT F

w2k, Hk =

∑ΩT F

ξ2k . (E18)

Ideally, the reconstructed signal energy in each detec-tor Hk should not significantly exceed the energy Ek.This requirement can be enforced by the constraint

Λk =∑ΩT F

wkξk − ξ2k = 0 (E19)

for each detector in the network. These constraints canbe applied during the signal reconstruction by way ofLagrange multipliers in the variational analysis, howeverthis greatly increases the computational complexity ofthe algorithm. A simpler alternative is to introduce apenalty factor Pf that penalizes sky locations violatingthe constraint equation (E19):

Pf = min

1,√E1

H1, ...,

√EKHK

. (E20)

In addition to serving as a penalty factor in the positionreconstruction, the ratio of reconstructed and detector

24

energy were also used as a post-production cut. Eventswith Pf < 0.6 were discarded, as were events with largevalues of the network energy disbalance

ΛNET =∑k

|Λk|Ecoh

, (E21)

and the H1-H2 energy disbalance

ΛHH =|ΛH1 − ΛH2|

Ecoh. (E22)

The latter cut was found to be particularly effective atrejecting correlated glitches in the two Hanford interfer-ometers.

The network correlation coefficient is also used toweight the overall likelihood for each sky location. Itis defined as

cc =Ecoh

Nnull + |Ecoh|(E23)

where Nnull is the sum of all elements in the null matrix

Nnm = Enm − Lnm , (E24)

which represents the normalized energy of the recon-structed noise. Usually for glitches little coherent energyis detected and the reconstructed detector responses areinconsistent with the detector output, which results in alarge value for the null energy. In addition to helping se-lect the optimal sky location, the correlation coefficientscc are used for a signal consistency test based on thecomparison of the null energy and the coherent energy.

The coherent terms of the likelihood matrix can be alsoused to calculate the correlation coefficients

rnm =Lnm√LnnLmm

(E25)

which represent Pearson’s correlation coefficients in thecase of aligned detectors. We use the coefficients rnm toconstruct the reduced coherent energy

ecorr =∑n 6=m

Lnm |rnm| . (E26)

Combined with the network correlation coefficient cc andthe number of detectors in the network, K, it yields aquantity which we call the coherent network amplitude,

η =√ecorr ccK

. (E27)

Figure 13 shows the η–cc distribution of the backgroundevents (see Sec. VI) and simulated GW events (seeSec. VII) for the L1H1H2 network. Loud backgroundevents due to detector glitches with low values of the net-work correlation coefficient are rejected by a threshold oncc. Relatively weak background events are rejected by athreshold on η. Table VI describes the full set of tuningparameters for cWB.

TABLE VI: Cuts used by the coherent WaveBurst pipeline inthe first year of S5. The parameters are: network correlationcoefficient cc, likelihood penalty factor Pf , coherent networkamplitude η, H1-H2 energy disbalance ΛHH , and network en-ergy disbalance ΛNET. Time-dependent cuts are noted withUTC times.

H1H2L1 Network

cc > 0.6 , Pf > 0.6

η > 5.7 for f<200 Hz, up to Dec 12 2005 03:19:29

or after Oct 25 2006 09:34:17

η > 5.2 for f<200 Hz, between Dec 12 2005 03:19:29

and Oct 25 2006 09:34:17

η > 4.25 for f>200 Hz

ΛHH < 0.3 , ΛNET < 0.35

H1H2 Network

cc > 0.65 , Pf > 0.6

η > 5.7 for f<200 Hz

η > 4.6 for f>200 Hz, up to Jul 17 2006 11:50:37

η > 4.25 for f>200 Hz, after Jul 17 2006 11:50:37

ΛHH < 0.3 , ΛNET < 0.35

H1L1 Network

cc > 0.6 , Pf > 0.6

η > 6.5 for f<200 Hz, up to Oct 07 2006 08:58:06

η > 9.0 for f<200 Hz, after Oct 07 2006 08:58:06

η > 5.0 for f>200 Hz

ΛNET < 0.35

H2L1 Network

cc > 0.6 , Pf > 0.6

η > 6.5 for f<200 Hz, up to Mar 28 2006 04:23:06

or after Oct 28 2006 11:54:46

η > 5.0 for f<200 Hz, between Mar 28 2006 04:23:06

and Oct 28 2006 11:54:46

η > 5.0 for f>200 Hz

ΛNET < 0.35

25

η

FIG. 13: Coherent network amplitude η [defined in Eq. (E27)]versus network correlation coefficient cc [defined in (E23)] forcWB triggers below 200 Hz in the H1H2L1 network. Theblack dots represent the noise triggers while the gray shadowsrepresent the distribution of a set of simulated GWs injectedinto the data. The horizontal and vertical bars represent thecuts on η and cc.

26

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